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STEAM ENGINE. 

Stationary — MARiiq^E — Locomotive — Gas Engines, Etc. 

THEORY OF STEAM ENGINE. 

Translated from the fourth edition of Weisbacli's Mechanics, 
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PUBLISHED AND FOB SALE BY 



JOHN WILEY & SONS, Astor Place, New York. 

*i)^Will 'be mailed, prepaid, on the receipt of the price. 



THERMODYNAMICS 



OF THE 



STEAM-ENGINE 



AND OTHER HEAT-ENGINES. 



BY 



CECIL H. PEABODY, 

Associate Professor of Steam Engineering, Massachusetts Institute of Technology. 



/5 



0.3/ 




NEW YORK: 
JOHN WILEY & SONS, 

15 AsTOR Place. 
1889. 






Copyright, 1889, 

BY 

CECIL H. PEABODY. 




Drcmmond & Neu, 

Electrotypers, 

1 to 7 Hague Street, 

New York. 



(^. nj^^ 



Ferris Bros., 

Printers, 

326 Pearl Street, 

New York. 



PREFACE, 



This work is designed to give instruction to students in 
technical schools in the methods and results of the application 
of thermodynamics to engineering. While it has been consid- 
ered desirable to follow commonly accepted methods, some parts 
differ from other text-books, either in substance or in manner 
of presentation, and may require a few words of explanation. 

The general theory or formal presentation of thermodynam- 
ics is that employed by the majority of writers, and was pre- 
pared with the view of presenting clearly the difficulties inher- 
ent in the subject, and of giving familiarity with the processes 
employed. 

In the discussion of the properties of gases and vapors the 
original experimental data on which the working equations, 
whether logical or empirical, must be based are given quite 
fully, to afford an idea of the degree of accuracy attainable in 
calculations made with their aid. Rowland's determination of 
the mechanical equivalent of heat has been adopted, and with 
it his determination of the specific heat of water at low tem- 
peratures. The author's '' Tables of the Properties of Satu- 
rated Steam and Other Vapors " were calculated to accompany 
this work, and may be considered to be an integral part of it. 

The chapters on the flow of gases and vapors and on the in- 
jector are believed to present some novel features, especially 
in the comparisons with experiments. 

The feature in which this book differs most from similar 
works is in the treatment of the steam-engine. It has been 
deemed advisable to avoid all approximate theories based on 
the assumption of adiabatic changes of steam in an engine cyl- 



IV PREFACE. 

inder, and instead to make a systematic study of steam-engine 
tests, with the view of finding what is actually known on the 
subject, and how future investigations and improvements may 
be made. For this purpose a large number of tests have been 
collected, arranged, and compared. Special attention is given 
to the investigations of the action of steam in the cylinder of 
an engine, considerable space being given to Hirn's researches 
and to experiments that provide the basis for them. Direc- 
tions are given for testing engines, and for designing simple 
and compound engines. 

Chapters have been added on compressed-air and refrigerat- 
ing machines, to provide for the study of these important sub- 
jects in connection with the theory of thermodynamics. 

Wherever direct quotations have been made, references have 
been given in foot-notes, to aid in more extended investiga- 
tions. It does not appear necessary to add other acknowledg- 
ment of assistance from well-known authors, further than to 
say that their writings have been diligently searched in the 
preparation of this book, since any text-book must be largely 
an adaptation of their work to the needs of instruction. 

C. H. P. 
Massachusetts Institute of Technology, 
May, 1889. 



TABLE OF CONTENTS. 



CHAPTER I. 

PAGE 

Thermal Capacities, ....... i 

CHAPTER II. 

First Law of Thermodynamics, . . , , . .11 

CHAPTER III. 
Second Law of Thermodynamics, . . , , • 19 

CHAPTER IV. 
Non-reversible Processes, . . . . . .34 

CHAPTER V. 

Fundamental Equations, ....... 37 

CHAPTER VI. 
Perfect Gases, ........ 45 

CHAPTER VII. 
Saturated Vapor, ....... i 68 

CHAPTER VIIL 

Superheated Steam, . . . . , , .115 

CHAPTER IX. 
Flow of Fluids, . • . . . . , , .129 

CHAPTER X. 
Injectors, ......... 144 

V 



vi TABLE OF CONTENTS. 

CHAPTER XI. 

PAGE 

Hot-air Engines, . . . . . . . .170 

CHAPTER Xn. 
The Steam-Engine, . . . . . . ... 178 

CHAPTER Xni. 
Compound Engines, ........ 204 

CHAPTER XIV. 
Testing Steam-Engines, . . . . « . . 225 

CHAPTER XV. 
Tests of Simple Steam-Engines, ...... 244 

CHAPTER XVI. 

Tests of Simple and Compound Engines, • . , . . 269. 

CHAPTER XVII. 
Hirn's Analysis, ........ 301 

CHAPTER XVIII. 
Various Steam-Engine Tests, ...... 338 

CHAPTER XIX. 

Friction of Engines, . . . . , , 395 

CHAPTER XX. 
Compressed Air, . ...... 405 

CHAPTER XXI. 
Refrigerating Machines, . . . . , , 434 



INDEX 



Absolute scale of temperature, 

Absolute scale of temperature and air thermometer, 

Absorption refrigerating apparatus, . 

Acceleration of gravity, . . . . 

Adiabatic expansion of vapor, external work, 

Adiabatic line for superheated steam, 

Adiabatic lines, . . . . " . 

Adiabatic lines for gases, . 

Adiabatic lines for vapor, construction of, 

Adiabatic of liquid and vapor, 

Alsatian experiments on friction of engines, . 

Alternative method. 

Ammonia, properties of, 

Application of first law, 

Application of first and second laws to gases. 

Application of first law to superheated steam. 

Application of second law. 

Application of second law to superheated steam, 

Air-compressor, calculation, . 

Air-compressor, compound. 

Air-compressor cylinder, volume of, . 

Air-compressor, displacement, 

Air-compressor, distribution of work, 

Air-compressor, effect of clearance. 

Air-compressor, fluid piston, . 

Air-compressor, power expended, 

Air-compressor, tests on. 

Air-engines, 

Air, Fleigner's equations of flow, 

Air-pumps, .... 

Air-refrigerating machine, 

Air thermometer, comparison with absolute scale, 

Air thermometer, reduction to absolute scale, 



25 

58 

460 

47 
III 
126 
14 
53 
109 
107 

30 
29 

456 
37 
48 

116 

39 
117 
418 
411 
410 
414 
416 
407 
413 
405 
415 
170 
135 
417 
434 
58 
60 



Vlll 



INDEX, 



Bache, tests on, .... 

Barrel calorimeter, 

Barrus continuous calorimeter, 

Barrus superheated steam calorimeter, 

Bell-Coleman refrigerating machine, . 

Boiler efficiency, .... 

British thermal unit. .... 

Calculations for compound engine, 
Calculations for triple-expansion engine. 
Calculation of air-compressor, 
Calculation of air-refrigerating machine. 
Calculation of compressed-air engine, 
Calculation of compression-refrigerating machine 
Calorimeter, .... 

Calorie, ...... 

Calorimeter, barrel, 

Calorimeter, continuous. 

Calorimeter, superheated steam, . 

Calorimeter, throttling. 

Capacities, thermal, 

Carnot's cycle for gases, 

Carnot's engine, .... 

Carnot's function, .... 

Carnot's principle, . .' . . 

Carnot's principle, generalization. 

Coefficient of dilatation, . . . , 

Characteristic equation. 

Characteristic equation for superheated steam, 

Characteristic equation, represented by a surface 

Closed cycle, .... 

Compressed air, .... 

Compressed air, contraction after compression. 
Compressed air, effect of clearance, . 
Compressed air, interchange of heat. 
Compressed air, temperature after compression, 
Compressed-air transmission, efficiency, . 
Compressed-air engine. 
Compressed-air engine, calculation. 
Compressed-air engine, compound. 
Compressed-air engine, consumption, 
Compressed-air engine, final temperature. 
Compressed-air engine, interchange of heat. 
Compressed-air engine, moisture in cylinder, 
Compressed-air engine, power of. 
Compressed-air engine, volume of cylinder, . 
Compression-refrigerating machine. 



PAGE 

268 



INDEX. 



IX 



Compound air-compressors, , 

Compound air-engine. 

Compound engine, 

Compound engine, calculations of, 

Compound engine, Hirn's analysis, 

Compound engine, ratio of cylinder, 

Compound engine, tests on, 

Compound engine with receiver, . 

Compound engine without receiver, . 

Condenser, ejector, 

Condensers, cooling surface, . 

Condensers, jet. 

Condensers, surface, 

Constants for superheated steam, . 

Continuous calorimeter, 

Cost of power. 

Critical temperature, . 

Cycle, closed, 

Cycle, reversible, 

Dallas, tests on, 

Density, .... 

Density of mercury. 

Density of vapors, 

Denton's tests of absorption refrigerating 

Designing steam-engines. 

Dexter, tests on. 



Differential coefficient 



dV 



Dilatation, coefficient of, . . ■ 

Distribution of engine friction, 

Dixwell's tests, 

Donkin engine tests, 

Donkin mill-engine, 

Donkin pumping-engine. 

Duty test of Leavitt engine, 

Dynamometers, 

Effects of the transfer of heat, 

Efficiency, .... 

Efficiency of boiler. 

Efficiency of compressed-air transmission 

Efficiency of ideal steam-engine, . 

Efficiency of reversible engines, 

Efficiency of steam-engine, 

Ejector, ..... 

Ejector condenser, . 

Emery, tests of engines. 



machine 



. 411 
429 

. 204 
212 

. 222 
210 

• 309 
207 

. 206 

167 
. 199 

199 
. ig6 

120 
. 231 

241 

. lOI 

22 
. 21 

269 

2 

76 

. 96 

469 

. 200 

269 

80, 82 

45 
. 400 

256 
. 338 

344 
. 346 

293 

. 227 

II 

. 22 

241 

• 432 
180 

. 28 
239, 366 
. 167 
167 
268, 271, 272 



INDEX. 



Energy, graphical representation of change 

Energy, intrinsic, superheated steam, 

English's steam-engine tests, . 

English's tests on initial condensation, 

Entropy, . . . 

Entropy of a liquid, 

Entropy of a liquid and vapor, 

Entropy of gases, .... 

Entropy of superheated steam. 

Entropy, scale of, . 

Engine, Carnot's, 

Engine, compressed-air, 

Engine, efficiency of, . 

Engine, efficiency of reversible 

Engine, Ericsson's, 

Engine, friction of, 

Engine, gas. 

Engine, hot-air, 

Engine, reversible. 

Engine, steam. 

Engine, Stirling's, 

Ericsson's hot-air engine, . 

Eutaw, tests on. 

Exhaust-steam injector, 

Experiments on flow of steam at Massachusetts Institute 

Exponent for superheated steam, , 

Exponential equation, .... 

External latent heat of vapors. 

External work during adiabatic expansion of vapor, 

Fan-blowers, ..... 

First and second laws combined. 

First law, application of, . 

First law, application to superheated steam, 

First law, application to vapors, 

First law of thermodynamics, 

Fleigner's equations for flow of air, . , 

Flow of air, Fleigner's equations, 

Flow of air, maximum velocity. 

Flow of air through porous plug. 

Flow of air, Weisbach's experiments, 

Flow of fluids, ..... 

Flow of gases, ..... 

Flow of incompressible fluids. 

Flow of saturated vapor, .... 

Flow of superheated steam. 

Fluid piston air-compressor. 



o 


PAGE 

. i6 




123 


, 


'■ 351 


• 


359 

. 17 

106 


. 


. 105 




55 


• 


. 119 
26 


• 


. 19 
425 


, 


. 22 




28 


. 


. 175 


■ . ■ . ■ 


395 
. 176 




170 
. 21 




178 


. 


. 172 




175 




• 253 
162 


e of Technology, 
II 


. 140 

7, 119 
. 102 




91 
. Ill 




414 


. 


• 41 




37 
. 116 




93 
II 




135 


• 


. 135 
136 


. 


. 59 




137 


. 


. 129 




131 


• 


. 129 

138 


. 


. 141 


. 


413 



INDEX. 



XI 



Fluids, flow of, . 

Fluids for refrigerating machines, 

Friction of engines, .... 

Friction of engines, Alsatian experiments, 

Friction of engines, Thurston's experiments. 

Function, Carnot's, 

Fundamental equations, 

Gas-engines, 

Gases, 

Gases, adiabatic lines, 

Gases, Carnot's cycle, . 

Gases, entropy. 

Gases, flow of, . 

Gases, general equations, . 

Gases, intrinsic energy, 

Gases, isodynamic lines, 

Gases, isoenergic lines, 

Gases, isothermal lines. 

Gases, ratio of specific heats. 

Gases, specific heat. 

Gases, specific volume, 

Gases, thermal capacities, . 

Gallatin, tests on. 

Gauges, 

General equations, 

General equations for gases, 

General equations, superheated steam, 

Giffard injector, .... 

Gleam, tests on, 

Graphical representation of change of energy 

Gravity, acceleration of, 

Hallauer's method of calculation, . 

Hallauer's tests of compound engines, 

Hallauer's tests of marine engines, 

Hallauer's tests of simple engines, 

Hancock injector, . 

Harris-Corliss engine, tests on, 

Heat, effects of transfer, . 

Heat, latent, of expansion. 

Heat, mechanical equivalent. 

Heat of the liquid. 

Heat, specific, 

Hill, tests on engines, . 

Hirn's analysis, calculation of problem 

Hirn's analysis for compound engine, 

Hirn's analysis for steam-engine, . 



PAGE 
129 

• 450 

395 

396 

. 400 

24 

• 37 
176 

. 45 
53 

. 55 
55 

. 131 
50 
55 

. 52 
52 

• 51 
63 
48 

. 46 

49 

. 273 

227 

. 6 

50 

.118 

154 

. 283 

16 

. 47 

304 

- 309 

309 

. 301 

156 

. 263 

II 

. 6 

II 

82, 84 

6 

• 263 
191 

. 222 
185 



Xll 



INDEX. 



Hirn's analysis, tests of engines, 

Hirn's experiments on superheated steam, 

Hot-air engine, Ericsson's, . 

Hot-air engine, Stirling's, 

Hot-air engines, 

Hot-air engines of maximum efficiency, 

Indicated steam consumption, 

Indicators, .... 

Injector, 

Injector as a pump. 

Injector, automatic, 

Injector, double, 

Injector, exhaust steam. 

Injector, fixed nozzle. 

Injector, Giffard's, 

Injector, Hancock, 

Injector, Korting, 

Injector, Mack, 

Injector, limits of action. 

Injector, Sellers, 

Injector, sizes of orifices, 

Injector, tests of, . 

Injector, theory of, 

Injector, velocity of steam jet. 

Injector, velocity of water jet. 

Injector, water, 

Injector, water fed per pound of steam, 

Initial condensation, 

Interchange of heat, compressed-air engine, 

Interchange of heat in air-compressors, 

Internal latent heat vapors, 

Intrinsic energy of gases, . 

Intrinsic energy of superheated steam, 

Isodynamic lines, . . ,• 

Isodynamic line for gases, 

Isodynamic line for steam, 

Isodynamic line for superheated steam, 

Isodynamic line for vapors, 

Isoenergic line for gases, 

Isoenergic line for steam, 

Isoenergic line for superheated steam, 

Isoenergic line for vapors. 

Isometric lines, 

Isopiestic lines, 

Isherwood, .... 

Isothermal lines. 



INDEX. 



Xlll 



Isothermal line for gases, , 

Isothermal for steam, 

Isothermal line for superheated steam 

Isothermal for vapors, 

Jet condensers, . 

Joule and Thomson's experiments, 

Joule's equivalent. 

Kilogram, weight of, 

Korting injector, 

Kraft's tests of air- compressors. 

Latent heat of expansion, 

Leavitt pumping-engine, 

Leila, tests on, . 

Length of meter. 

Line of constant steam weight, 

Lines, adiabatic. 

Lines, isoenergic, 

Lines, isopiestic, 

Lines, isometric. 

Lines, isothermal, . 

Lines, thermal, . . . 

Liquid and vapor, adiabatic line, . 

Liquid, entropy of, 

Liquids, specific volumes of. 

Mack injector, . 

Mackinaw, .... 

Mair's steam-engine tests. 

Marine engines, tests on, 

Massachusetts Institute of Technology steam-engine tests 

Massachusetts Institute of Technology experiments on flow of steam 

Massachusetts Institute of Technology tests of injectors, 



Massachusetts Institute of Technology tests on steam 

Maximum velocity of flow of air, . 

Mechanical equivalent. Joule's, 

Mechanical equivalent, Rowland's, . 

Mechanical equivalent of heat, . 

Mercury, density of, 

Meter, length of, 

Michigan, tests on, . 

Millers' exhibition, 

Napier's formulae for flow of steam, 

Non-reversible processes, . 

Pambour's method, friction of engines 

Perfect gases, 

Pictet's fluid. 

Porous plug, flow through, 



engmes 



PAGE 

51 
103 
127 
103 
199 

59 

88 

76 

157 

415 

6 

293 

283 

76 

102 

14 

13 

13 

13 

13 

13 

107 

106 

90 

153 

249 

318 

309 

333 
140 

159 

385 

136 

. 88 

85 
II, 87 

76 

. 76 

244 

• 263 

. 140 

34 
. 395 

45 
. 459 

59 



XIV 



INDEX. 



Power, cost of, . 

Power expended in compressing air. 

Power of compressed-air engine, 

Pressure, effect of, on change of state. 

Pressure of saturated steam, 

Pressure of steam at Paris, 

Pressure of vapors, 

Pressure, specific, .... 

Principle, Carnot's, 

Processes, non-reversible, . 

Rankine's equation for pressure of steam, 

Ratio of cylinders, compound engines, 

Ratio of specific heats, . 

Regnault's equations for steam, 

Refrigerating machines. 

Refrigerating machines, absorption, 

Refrigerating machines, air, 

Refrigerating machines, calculation, 

Refrigerating machines, compression. 

Refrigerating machines, extraction of moisture 

Refrigerating machines, fluids. 

Refrigerating machines, vacuum, . 

Refrigerator, .... 

Relations of thermal capacities, 

Reversible cycle, .... 

Reversible engine, .... 

Reversible engines, efficiency of, 

Reynolds-Corliss engine. 

Rotary blowers, 

Rowland's experiments, 

Rowland's equivalent, . 

Rowland, reduction of air thermometer, . 

Rush, tests on, .... 

Saturated vapor, flow of, . 

Saturated vapors, 

Scale of entropy, .... 

Scales, ..... 

Schroter's tests of refrigerating machines, . 

Seaton's multipliers for steam-engine design, 

Second law, application of. 

Second law, application to superheated steam, 

Second law, application to vapors, . 

Sellers injector, .... 

Siesta, tests on, .... 

Sound, velocity of, . 

Source of heat, .... 



PAGE 

. 241 
405 

• 425 
lor 

75, 76 

73 

68, 79 

2, 47 

. 23 

34 

. 78 

210 

. 63 

71 

. 434 

460 

• 434 
438, 446 

. 444 
437 

• 450 
462 

• 19 
7 

. 21 

21 

. 28 

263 

. 414 

85 
. 88 

60 

. 269 

138 

. 68 

26 
. 228 

463 
r, 221 

39 

. 117 

94 

. 154 

283 

. 60 

19 



INDEX, 



XV 



specific heat, ...... 

Specific heat of gases, .... 

Specific heat of superheated steam at constant volume. 

Specific heat of steam, 

Specific heat of water, 

Specific heat of vapors, 

Specific heats of gases, ratio, . 

Specific heats of water and steam, , 

Specific pressure. 

Specific volume, .... 

Specific volume of gases, 

Specific volume of vapors, . 

Specific volumes of hot liquids, 

Standard temperature. 

Steam, application of first law. 

Steam, application of second law, . 

Steam consumption, measurement of, . 

Steam, curve of constant weight, . 

Steam, entropy of, . 

Steam, flow of, . . . . 

Steam, internal and external heat, 

Steam isodynamic line, 

Steam isoenergic line, . 

Steam, isothermal, .... 

Steam, Napier's equations for flow. 

Steam, pressure of, . 

Steam, pressure at Paris, 

Steam, Rankine's equation, 

Steam, Regnault's equations, . 

Steam, specific heat of, . 

Steam, superheated. 

Steam, total heat, .... 

Steam-engine, .... 

Steam-engine, actual, 
Steam-engine, Carnot's cycle, . 
Steam-engine, compound, . 
Steam-engine, consumption for perfect cycle, 
Steam engine designing, 
Steam-engine efliciency. 
Steam-engine indicators, 
Steam-engine, Hirn's analysis, . 
Steam-engine, testing of, . 
Steam-engine, Seaton's multipliers, 
Steam-engine, triple and quadruple expansion 
Steam-engine, water in the cylinder, 
Stirling's hot-air engine. 



PAGE 

. 6 

48 
. 122 

95 
82, 86 

95 

• 63 
93 

2, 47 

2 

. 46 

96 
. 90 

87 

• 93 
94 

. 229 
102 

. 105 
138 

• 91 
104 

. 104 

103 

. 140 

75, 76 

. 73 

78 

. 71 

95 

• 115 

88 
. 178 

181 
. 178 

204 
. 180 

200 
. 239 

228 
. 185 

225 
. 201 

209 
. 333 

172 



XVI 



INDEX. 



Superheated steam, .... 

Superheated steam adiabatic line, , 

Superheated steam, application of first law. 

Superheated steam, application of second law. 

Superheated steam, characteristic equation, 

Superheated steam, comparison with experiments, 

Superheated steam, entropy, 

Superheated steam, flow of, . . 

Superheated steam, general equations, 

Superheated steam, Hirn's experiments, . 

Superheated steam, intrinsic volume, . 

Superheated steam, isodynamic line. 

Superheated steam, isoenergic line, 

Superheated steam, isothermal line, 

Superheated steam, specific heat at constant volume, 

Superheated steam, thermal capacities, 

Superheated steam, total heat, . 

Superheated steam, values of constants, 

Sulphur dioxide, properties of. 

Surface condensers, 

Tate and Fairbairn's experiments, 

Temperature, .... 

Temperature, absolute scale of. 

Temperature, definition of, 

Temperature, standard, 

Temperature, Thomson's scale. 

Testing steam-engines, . 

Tests of absorption-refrigerating machine. 

Tests of air-compressors, 

Tests of Bell-Coleman refrigerating machine, 

Tests of compression -refrigerating machines, 

Tests of injectors, . . » . 

Tests of refrigerating machines, Schroter, 

Tests of Sellers' injector, 

Tests on automatic engines, 

Tests on Donkin engines, . 

Tests on Donkin mill-engine, . 

Tests on Donkin pumping- engine, . 

Tests on compound engines, 

Tests on Leavitt engine. 

Tests on marine engines. 

Tests on initial condensation, 

Tests on simple steam-engines, 

Tests on simple and compound engines, 

Tests on steam-engines, Dixwell's, 

Tests on steam-engines, Mair's, 



INDEX. 



XVll 



Tests on steam-engines, English's, 

Tests on steam-engines, Institute of Technology, 

Tests on steam-engines, various. 

Tests on the Bache, 

Tests on the Eutaw, 

Tests on the Gallatin, 

Tests on the Leila, Siesta, and Gleam, 

Tests on the Mackinaw, 

Tests on the Michigan, . 

Tests on the Rush, Dexter, and Dallas, 

Tests on Willans' engine. 

Tests on Worthington pumping-engine, 

Theory of injectors, 

Thermal capacities, . 

Thermal capacities of gases. 

Thermal capacities, relations of, 

Thermal capacities, superheated steam, 

Thermal lines, 

Thermal unit, .... 

Thermodynamics, first law. 

Thermodynamics, second law, . 

Thermometers, 

Thomson's scale of temperature, 

Thomson and Joule's experiments. 

Throttling calorimeter, . 

Thurston's experiments on friction of engines, 

Total heat of steam. 

Total heat of superheated steam, . 

Total heat of vapors. 

Triple-expansion engine, calculations, 

Triple-expansion engines, 

Unwin, test of pumping-engine. 

Vacuum refrigerating apparatus. 

Value oi R, . 

Vapor and liquid, adiabatic line, 

Vapor, entropy of, . 

Vapor, flow of, . . . , 

Vapors, .... 

Vapors, application of, . 

Vapors, application of first law. 

Vapors, density of, . 

Vapors, internal and external heat. 

Vapors, isodynamic line, 

Vapors, isoenergic line. 

Vapors, isothermal line, 

Vapors, pressure of, , , 



PAGE 

333. 385 
. 338 

268 
. 253 

272 
. 283 

249 
. 244 

269 

• 364 
387 

. 146 

5 

• 49 

6 
. 118 

13 

. II 

II 

I9» 23 

227 

. 25 

59 

. 237 

400 
. 88 

123 
. 88 

220 
. 209 

387 
. ^^62 

47 

. 107 

105 

. 138 

68 

. 94 

93 

. 96 

91 

. 104 

104 

. 103 

68, 79 



XVlll 



INDEX. 



Vapors, specific heat, . , • 

Vapors, specific volume of, , 

Vapors, total heat. 

Velocity of sound, . 

Volume of air-compressor cylinder, 

Volume of compressed-air engine cylinder 

Volume, specific. 

Water in the cylinder of steam-engines, 

Water, specific heat of. 

Water injector. 

Weight of kilogram, 

Weirs, . . . 

Weisbach's experiments on flow of air, 

Wheelock engine, tests on, 

Willans' steam-engine tests, 

Zeuner's equations, . 

Zeuner's equations for internal heat, • 



95 

96 

89 

60 

410 

428 

2 

333 
82 

165 
76 

228 

137 
263 

364 

42 

100 



THERMODYNAMICS OF THE STEAM-ENGINE. 



CHAPTER I. 

THERMAL CAPACITIES. 

The object of thermodynamics, or the mechanical theory 
of heat, is the solution of problems involving the action of 
heat, and, for the engineer, more especially those problems pre- 
sented by the steam-engine and other thermal motors. In this 
work the discussion of the actual nature of heat and the 
rationale of its various actions will be purposely avoided, and 
attention will be given rather to the calculation of the results 
of such actions. 

Some conceptions already familiar will appear in a some- 
what different light ; and some new conceptions will be pre- 
sented. It will be found that some of the latter are susceptible 
of more concise definition than others that are now more 
familiar. Also some methods of operation will be employed 
which may seem more abstract than those commonly used in 
engineering. The student will, however, recognize them as 
methods that he has already learned, and he will gain confi- 
dence in them by familiarizing himself with their use. 

Effects of Heat. — In general, the action of heat on a 
body causes a change in all the characteristics of the body, such 
as the density, tension, temperature, elasticity, refractive 
index, conductivity, etc. When heat is communicated to or 
taken from a body, there is a change in the energy of the body. 
If a body is supposed to be at rest, or if its visible motion is 
not changed during the operation, and can consequently be 
disregarded, the change of energy produced by the communi- 



2 THERMODYNAMICS OF THE STEAM-ENGINE. 

cation or abstraction of heat may be considered as a property 
of the body. The energy may in general be divided into 
potential and kinetic energy, in which case each may be a prop- 
erty of the body. 

Characteristic Equation. — The assumption of the me- 
chanical theory of heat is that if any two of the several 
characteristics or properties of a body be taken as independent 
variables, any other can be expressed as a function of the two 
independent variables. If x and y are chosen as the independ- 
ent variables, and if z is any other characteristic, then 

z — F{x, j), or /{x, y, z) = o. 

The form of the function is to be determined experimentally : 
and as yet the necessary experiments have been made for only 
a few of the numerous functions that may be indicated by 
using the various characteristics. The most useful character- 
istic equation is 

/{p,v,t) = o, (i) 



in which/ is the pressure, v the volume, and / the temperature. 

The pressure is assumed to be a hydrostatic pressure, such 
as a fluid exerts on the sides of the containing vessel or on an 
immersed body. We shall always consider the pressure exerted 
dy the body rather than on the body. The pressure is stated 
in units of force per unit of area, as pounds per square foot, 
and is called specific pressure. 

The density of a body is the weight of a unit of volume ; 
for example, a cubic foot of water weighs 62.4 pounds nearly, 
or its density is 62.4. The reciprocal of the density is the 
volume occupied by one unit of weight, and is called the specific 

volume ; the specific volume of water being -p — . 

The temperature cannot be as satisfactorily defined. The 
common scales depend on the properties of some substance, 
such as mercury or air ; and it can be shown that the unit is 



THERMAL CAPACITIES. 3 

not the same in different parts of the scale. In the course of 
the work it will be shown that an absolute scale independent 
of the substances used can be constructed on thermodynamic 
principles. It will also appear that the scale of the air ther- 
mometer coincides very nearly with the thermodynamic scale. 
Again, the scale of the. mercurial thermometer at medium 
temperature agrees with that of the air thermometer sufficiently 
well for engineering work. To avoid difficulty that may arise 
when we are ready to establish the thermodynamic scale, we 
will abstain from accepting any ^cale even temporarily. 

It will be sufficient to fix the two following ideas of tem- 
perature : 

(i) Of two bodies in thermal communication (by conduction 
or radiation), that one which imparts heat to the other is at the 
higher temperature. If neither gains or loses, they are at the 
same temperature. 

(2) There are certain temperatures, such as the freezing and 
boiling points of water at atmospheric pressure, which are fixed 
and can be identified. We may assume that there are a series 
of such fixed temperatures, natural or artificial, which may be 
compared to a scale of hardness ; and we may say that the 
temperature of a body coincides with one of them, or is higher 
than one and lower than another. We may, if we choose, use 
the air thermometer for the purpose; but in such case the 
degrees are to be considered as fixed points and not as units of 
measurement. 

We may, however, admit that a true scale is possible, and 
that temperature may enter into an equation, but that the form 
of the function remains to be determined. 

To give a concrete meaning to the characteristic equation, 
we may refer to the combined law of Boyle and Gay Lussac for 
a perfect gas. If we accept for the moment the scale of the 
air thermometer, the law may be represented by the equation 

P' = ^- + t)R, (2) 

in which i? is a constant, a is the coefficient of dilatation of 



4 THERMODYNAMICS OF THE STEAM-ENGINE. 

air, and t is the temperature by the air thermometer on the Cen~ 
tigrade scale. Transposing, 

[/^-£ + ^)^]=o (3) 

This is the characteristic equation for a perfect gas in terms 
of/, v^ and /, in which a may be assumed to be constant. 

The value of a is very nearly — . Consequently, if we 

make — h ^ = 273.7 + ^ = 7", we shall have, instead of (3), 

pv — RT—O (4) 

The letter T is used to represent what is sometimes called 
the absolute temperature of the air thermometer above the 
absolute zero. 

Now, air near the freezing point of water expands of 

its volume at freezing for each degree of increase of tempera- 
ture, and also contracts of its volume for each degree 

273.7 ^ 

below freezing. If the thermometer be formed of a tube of 
uniform calibre, and the space between freezing and boiling be 
divided into one hundred parts, and if the division be continued 
to the closed ends, there will be 273.7 divisions below freezing 
point. The degrees may be numbered beginning at the closed 
end ; and the temperatures on such scale will be represented by 

r= 273.7 + A 

Now, any equation with three variables may be represented 
by a geometrical surface, referred to co-ordinate axes, of which 
surface the variables are the co-ordinates. In the case of a 
perfect gas which conforms to the equation 

pv^RT, 



THERMAL CAPACITIES. 




Fig. 



the surface is such that each section perpendicular to the T is 
a rectangular hyperbola (Fig. i). 

Returning now to the general case, 
and abstaining from adopting any spe- 
cific scale of temperature, it is apparent 
that the characteristic equation of any 
substance may be represented by a 
geometrical surface referred to co-ordi- 
nate axes, since the equation is assumed 
to contain only three variables ; but the 
surface will in general be less simple in form than that repre- 
senting the combined law of Boyle and Gay Lussac. 

If one of the variables, as /, is given a special constant value, 
it is equivalent to taking a section perpendicular to the axis of 
t ; and a plane curve will be cut from the surface, which may 
be conveniently projected on the (/, v) plane. 

Sections may be taken perpendicular to the other axes, and 
a sufficient number of such sections, or, as a substitute, the pro- 
jections of the intersections, will give a complete description of 
the surface. The whole process is equivalent to a complete 
solution of the characteristic equation, but there are few sub- 
stances of which the properties are sufficiently well known for 
the purpose. 

Other curves in addition to the sections may be drawn on 
the surface and projected on the (/, v) plane. It is essential 
sometimes to distinguish between the actual curve and its pro- 
jection. The reason for choosing the (/>, v) plane is that the 
curves drawn correspond to those drawn by the indicator. 

Thermal Capacities. — The amount of heat required to 
change by unity any quality of a unit of weight of any body 
under given circumstances is called the thermal capacity corre- 
sponding to the given change. 

In three cases only have these capacities received special 
names ; i.e.^ specific heat at constant volume, specific heat at 
constant pressure, and latent heat of expansion. 

Thermal Unit. — Heat is measured in calories, or British 
thermal units (B. T. U.). A calorie commonly is defined as the 



6 THERMODYNAMICS OF THE STEAM-ENGINE. 

heat required to raise one kilogram of water from freezing- 
point to one degree Centigrade ; and a British thermal unit, 
that required to raise one pound from 32° to 33*^ Fahrenheit. 
In our work, for reasons that will appear in the discussion of 
the specific heat of water, we shall choose 62° F. for the stand- 
ard temperature, and shall define a B. T. U.as the heat required 
to raise a pound of water from 62° to 63° F. 

This statement is subject to the same indefiniteness as the 
thermal scale from which it is derived. The true value can be 
defined only after a logical thermal scale is developed. 

Specific Heat is the heat required to raise one unit of 
weight of a substance through one degree of temperature, 
measured in thermal units. The specific heat of water at the 
standard temperature is consequently unity. Two specific 
heats are commonly distinguished ; at constant pressure Cp , and 
constant volume c^ . Both of these specific heats are liable to 
be variable ; consequently, if the amount of heat dQ imparted 
to a unit of weight of a substance changes the temperature by 

dl, then the specific heat at a given temperature ^ is ^ = -y-. 

If the change takes place at constant pressure or at constant 
volume, then 

dQ\ Id0\ 

-r-] or c^— \~~\ 

(I'V I p constant, N ^^ ' v constant. 

Latent Heat of Expansion is the amount of heat required 
to change the volume of one unit of weight by the amount of 
one unit. 

As this property is also sometimes variable, we may prop- 
erly write for the latent heat of expansion at the temperature /, 



\avl i 



General Equations of the Effects produced by Heat. — 

The heat given to a body and which produces a certain chanr^e 



THERMAL CAPACITIES, J 

in that body may be a function of /, v, and /. If v and t are 
chosen for the independent variables, then 

"^ =©/'+©/- <'•) 

In like manner, with / and t as independent variables, 

"e-rD/'+di*^ («^) 

and with/ and v as independent variables, 

"eHD/'+lf)/" <"> 

Substituting for (-7-) , in equation (5a), the specific heat at 
constant volume, and for \~r']^ the latent heat of expansion, 

dQ = c^dt + Idv (5) 

In like manner the specific heat at constant pressure may 
be substituted for \-t.\ hi equation (6a); and for \~r-] may be 

substituted /, which represents the amount of heat required to 
be added when the external pressure is increased by unity, a 
thermal capacity which has not as yet received a name ; 
whence 

dQ = cpdt -\- mdp (6) 

Finally, (~^-) may be represented by n, and {-f] by 0, 

both being thermal capacities without names, and equation (7a) 
becomes 

dQ — ndp + odv (7) 

Relations of the Thermal Capacities. — The three equa- 
tions, (5), (6), and (7), show the changes produced by the addi- 



8 THERMODYNAMICS OF THE STEAM-ENGINE. 

tion of an amount of heat dQ to a unit of weight of a substance, 
the difference coming from the methods of analyzing the 
changes, but the total amount dQ may be the same in all ; con- 
sequently the left-hand members maybe equated, forming three 
equations. Thus, equating (5) and (6), 

c^dt ■\- Idv = Cpdt -f- mdp (8) 

From the general characteristic equation we have 

from which, by differentiating, we have 

which substituted in (8) gives 

c,dt + mdp = cjt + ^[©/^+(J)//]. 

... Cpdt + mdp = \^,, + l[jj)'yt + ^(^)//- • • (9) 

In equation (9) p and / are independent variables, and each 
may have all possible values; consequently we may equate like 
coefficients. 

it If 

'p 






Again, equating the remaining coefficients, 

In like manner, by differentiating the general equation, 



THERMAL CAPACITIES. 9 

which substituted in (8) gives 

Equating like coefficients, 

'> + KJ) = ^- ..... (14) 



or 

— m 



Equating (6) and (7), 
Substituting from 



Equating coefficients of dv, 

"^^S)/- ••••••• (17) 

Finally, equating (5) and (7), 

<:j,<3f/ -|- /</z/ = ndp -\- odv. 
Substituting for the value of dt^ as above, 
fdt \ , idt 



c. 



\~r\ ^'^ ~\~ ^A~Jfyi ^P + ^'^^ — ^^P + ^^^* 



lO THERMODYNAMICS OF THE STEAM-ENGINE. 

Equating coefficients of dp, 

jdt 
c. 



©. (-) 



In the preceding work we have six coefficients, c^, c^, /, 

m^ It, and o, of which Cp is commonly known for any substance. 

The coefficient c^ cannot be readily determined directly, but 

the ratio — - = /c is known for some substances, especially gases, 

and from it c^ may be found. The other four are expressed in 
terms of the specific heats, which for convenience are here 
assembled : 



Idt \ fdt \ 



Jdv 

m = / — - 

\dp 



Also we have in general for three variables, as/, v, and /, 



^dt I Tj ^dp ' t \dv ' p 



also, 

'dt \ (dp \ idv 



© 



dp I ^ \dvit \dtij, ^ ^ 

The relations thus far deduced are merely necessary alge- 
braic relations of the literal functions, and are related to the 
theory of heat since the forms are those that appear in that 
theory. They are therefore true, whatever theory be accepted 
and whatever scale of temperature be adopted. 



CHAPTER II. 

FIRST LAW OF THERMODYNAMICS. 

The formal statement of the first law of thermodynamics is: 
Heat and mecJiaitical energy are mutually convertible, and 
heat requires for its production and produces by its disappearance 
a definite number of units of work for each thermal unit. 

The mechanical equivalent of heat is designated by^, and 
the reciprocal by A ; so that 

^=7 •• • (^■> 

The value of the mechanical equivalent of heat given by 
Joule, and long quoted in all works on heat, is 772 foot-pounds 
for one B.T.U. In the French system the equivalent of one 
calorie, corresponding, is taken to be 424 meter-kilograms. 

The value of f determined by Rowland at 62° F. or 
i6|° C. and reduced to 45° of latitude, is^ for 

I B.T.U., 778 foot-pounds ; 

I calorie, 426.9 meter-kilograms ; 

and these values will be used in our work unless the contrary 
is stipulated. 

This law is a special statement of the general law that 
energy can neither be created nor destroyed, but may be trans- 
muted from one form to another, with a definite number of 
units in one form, equivalent to a given number in the other. 
The law is a physical and experimental law, differing essentially 
from an axiom. 

Effects of the Transfer of Heat. — Let a quantity of any 
substance of which the weight is one unit, i.e., one pound or 
one kilogram, receive a quantity of heat dQ. It will, in general, 
experience three changes, each requiring an expenditure of 

II 



12 THERMODYNAMICS OF THE STEAM-ENGINE. 

energy. They are : (i) The temperature will be raised, and, by 
the theory that sensible heat is due to the vibrations of the 
particles of the body, the kinetic energy will be increased. Let 
dS represent this change of sensible heat or vibration work in 
units of work. (2) The mean positions of the particles will be 
changed ; in general the body will expand. Let dl represent 
the units of work required for this change of internal potential 
energy, or work of disgregation. (3) The expansion indicated 
in (2) is generally against an external pressure, and to overcome 
the same, that is, for the change in external potential energy, 
there will be required the work dW. 

If during the transmission no heat is lost, and if no heat is 
transformed into other -forms of energy, such as sound, elec- 
tricity, etc., then the first law of thermodynamics gives 

dQ = A{dS^dI-^dW) (22) 

It is to be understood that any or all of the terms of the 
equation may become zero or may be negative. If all the 
terms become negative, heat is withdrawn instead of added, 
and dQ is negative. It is not easy to distinguish between the 
vibration work and the disgregation work, and for many pur- 
poses it is unnecessary; consequently they are treated together 
under the name of intrinsic energy, and we have 

dQ^A {dS + dI-\- dW) :=.A{dE-{- dW). . . (23) 

The inner work, or intrinsic energy, depends on the state of 
the body, and not at all on the manner by which it arrived at 
that state ; just as the total energy of a falling body, with refer- 
ence to a given plane consisting of kinetic energy and potential 
energy, depends on the velocity of the body and the height 
above the plane, and not on the previous history of the body. 

The external work is assumed to be done against a fluid 
pressure ; consequently 

dW — pdv, (24) 

W^ r^pdv, (25) 

where n and v^ are the final and initial volumes. 



FIRST LAW OF THERMODYNAMICS, 1 3 

This assumption holds good when the substance itself is a 
fluid ; for example, the steam in the cylinder of an engine. 

In order to find the value of the integral v, in equation (25), 
it is necessary to know the manner in which the pressure varies 
with the volume. 

Since the pressure may vary in different ways, the external 
work cannot be determined from the initial and final states of 
the body. The heat required to effect a change from one state 
to another depends on how the change is effected. 

Assuming the law of the variation of the pressure and volume 
to be known, we may integrate thus : 

Q=A(E,-E„ + £ydvy .... (26) 

In order to determine E for any state of a body, it would 
be necessary to deprive it entirely of vibration and disgregation 
energy, which of course involves reducing it to a state of ab- 
solute cold. Consequently the direct determination is impossi- 
ble. However, in all our work the substances operated on are 
changed from one state to another, and in each state the intrin- 
sic energy depends bn the state only ; consequently the change 
of intrinsic energy may be determined from the initial and final 
states only, without knowing the manner of change from one to 
the other. 

All succeeding equations will be arranged to involve differ- 
ences of energy only, and the hypothesis involved in a separa- 
tion into vibration and disgregation work avoided. 

Thermal Lines. — The external work can be determined 
only when the relations of p and v are known, or, in general, 
when the characteristic equation is known. It has already been 
shown that in such case the equation may be represented by a 
geometrical surface, on which so-called thermal lines can be 
drawn representing the properties of the substance under con- 
sideration. These lines are commonly projected on the (/, v) 
plane. It is convenient in many cases to find the relation of / 
and V under a given condition and represent it by a curve drawn 
directly on the (/, v) plane. 



14 THERMODYNAMICS OF THE STEAM-ENGINE. 

A number of the thermal lines will be thus represented and 
p discussed. 

*" ^" hopiestic lines, or lines of equal pressure. — The 

change of condition takes place at constant press- 
ure, and consists of a change of volume, as repre- 
sented in Fig. 2. The tracing point moves from 
Fig. 2. a^ to a^, and the volume changes from v^ to v^. 
The work done is represented by the rectangular area under 
a,a^, or by 



W — pl ^^dv = p{v^ — v^. 

t/Vr, 



During the change the temperature may or may not change ; 
the diagram shows nothing concerning it. 

Isometric lines, or lines of equal volume. — The 
^1 pressure increases at constant volume, and the 
a^ tracing point moves from a^ to a^. The tempera- 
ture usually increases meanwhile. Since dv is zero, 



Fig. 



== / ^pdv 



W — I 'pdv = o. 



Isothermal lines, or lines of equal temperature. — The tem- 
perature remains constant, and a line is drawn, usually convex, 
toward the axis OV. The pressure of a mixture of a liquid and 
its vapor is constant for a given temperature ; consequently the 
isothermal for such a mixture is a line of equal pressure, repre- 
sented by Fig. 2. The isothermal of a perfect 
gas, on the other hand, is an equilateral hyper- 
bola, as appears from the law of Boyle, which 
may be written 

Fig. 4. pV = C, (2/) 

Isodynamic or isoenergic lines are lines representing changes 
during which the intrinsic energy remains constant. Conse- 
quently all the heat received is transformed into external work. 
It will be seen later that the isodynamic and isothermal lines 
for a p:as are the same. 




FIRST LAW OF THERMODYNAMICS, 1 5 

Adiabatic Lines. — A very important problem in thermody- 
namics is to determine the behavior of a body when change of 
condition occurs without gain or loss of heat ; that is, such a 
change as would occur in a perfectly non-conducting vessel. 
During the change heat may be transformed into work, or vice 
versa ; but no heat is transferred in the form of heat. Direct 
experiments are very difficult, and are usually approximations ; 
very rapid changes in any vessel are nearly adiabatic, since time 
is required for conduction and radiation of heat. Rankine gave 
the name adiabatic to lines representing the volume and press- 
ure during changes that occur without transmission of heat. 
When there is no transmission of heat, equation (26) becomes 

o = q^a{e,-e, + JJ^' pdvy, 

consequently, 

- (£, - £,) = r^pdv, (28) 

which shows that work done by the body against external 
pressure is at the expense of the intrinsic energy. Since the 
two quantities are numerically equal, the sign may frequently 
be neglected in numerical problems. 

When an adiabatic crosses an isothermal, both being pro- 
jected on the (/, v) plane, it is the steeper, as shown at a^, 
Fig. 5. This is easily shown for substances that p 
expand with the rise of temperature. For, if a 
body expands in a non-conducting vessel, the 
external work done is at the expense of the in- 
trinsic energy, as shown by equation (28) ; and a 
diminution of the intrinsic energy in general is fig. 5. 

made up of a loss of potential energy, due to molecular ar- 
rangement, and a loss of kinetic energy, due to temperature. 

Now, a loss of temperature at constant pressure causes a 
contraction of volume ; or, conversely, at constant volume a 
loss of temperature causes a lowering of pressure. In Fig. 5 
an expansion at constant temperature is represented by the 
isothermal a^a^^ while an expansion without transmission of heat 




1 6 THERMODYNAMICS OF THE STEAM-ENGINE, 

is represented by the adiabatic a^a' . The final volume is the 
same ; consequently the pressure represented by a' is less, since 
the adiabatic expansion is accompanied by a loss of temperature. 
Graphical Representations of Change of Intrinsic 
Energy. — Professor Rankine first used a graphical method of 
representing a change of intrinsic energy, employing adiabatic 
lines only, as follows : 

Suppose that a substance is originally in the state A (Fig, 
6), and that it expands adiabatically ; then the external work 
is done at the expense of the intrinsic en- 
ergy; hence, if the expansion has proceeded 
to A^ , the area AA^a^a, which represents the 
external work, also represents the change of 
intrinsic energy. Suppose that the expan- 
sion were to continue indefinitely ; then the 
adiabatic will approach the axis OV indefi- 
nitely, and the area representing the work will be included 
between the curve A a produced indefinitely, the ordinate Aa, 
and the axis OV; this area will represent all the work that can 
be obtained by the expansion of the substance ; and if it be 
admitted that during the expansion all the intrinsic energy is 
transformed into work, so that at the end the intrinsic energy 
is zero, it represents also the intrinsic energy. In cases for which 
the equation of the adiabatic can be found, it is easy to show 
that 




B^ = 1^ pdv 



is a finite quantity ; and in any case, if we admit an absolute 
zero of temperature, it is evident that the intrinsic energy can- 
not be infinite. On the other hand, if an isothermal curve were 
treated in the same way, the area would be infinite, since heat 
would be continually added during the expansion. 

Now suppose the body to pass from the condition repre- 
sented by A to that represented by B, by any path whatever ; 
that is, by any succession of changes whatever ; for example, 
that represented by the irregular curve AB. The intrinsic 
energy in the state B is represented by the area VbBft. The 



F/A'ST LAW OF THERMODYNAMICS. 



17 




Fig. 7. 



change of intrinsic energy is represented by the area ftBbaAa^ 
and this area does not depend on the form of the curve AB. 
This graphical process is only another way of stating that the 
intrinsic energy depends on the state of the substance only, and 
that change of intrinsic energy depends on the final and initial 
states only. 

Another way of representing change of intrinsic energy by 
aid of isodynamic lines avoids an infinite diagram. Suppose 
the change of state to be represented by the 
curve AB, Fig. 7. Draw an isodynamic line 
AC through the point A, and an adiabatic 
line BC through B, intersecting at C. Then 
the area ABba represents the external work, 
and the area bBCc represents the change of 
intrinsic energy ; for if the body be allowed 
to expand adiabatically till the intrinsic energy is reduced to its 
original amount at the condition represented by^, the external 
work bBCc will be done at the expense of the intrinsic energy. 
Since the intrinsic energy is constant for all points on the 
isodynamic line through A, and in like manner is constant for 
points on the line through B, there will be the same change of 
intrinsic energy in passing from a condition represented by any 
point of the line through A to any point of the line through B ; 
consequently, if through any point, as D of the upper line, an 
adiabatic DE be drawn, the area dDEe will be equal to bBCc, 
and will equally represent the change of intrinsic energy from 
the point A to the point B. 

Entropy. — If a body have its condition represented by the 
point e of the isothermal . ^^^ (Fig- 8), it will have a definite 
temperature, which will be the same so long as 
its condition is represented by some point on 
aa^ , as, for example, a^ , though the volume and 
pressure will meanwhile have varied. Should 
the temperature change, the condition will be 
represented by some point, as /, on another 
isothermal bb^ . There will evidently be the 
same change of temperature in passing from ^ to/ as from e^ 




Fig. 8. 




1 8 THERMODYNAMICS OF THE STEAM-ENGINE. 

to /i ; that the changes of volume and pressure, external work, 
and intrinsic energy are different does not affect the statement 
concerning the temperature. In Hke manner, it is indifferent 
how or at what part of the diagram the transfer from bb^ to cc^ 
is accompUshed ; the same change of temperature must occur. 
Let aa^, bb[, and ^^j represent adiabatic Hnes. 
Then if a body having its condition represented 
by a point on aa^ experience a change repre- 
sented by ee^ , it will have neither lost nor gained 
heat as such, though heat may have been 
~ changed into work ; or, vice versa, any change 
that can be represented by a portion of an adia- 
batic line will be subject to the same condition. There is, 
we see, some property of the body that remains constant 
during an adiabatic change ; and that property is called the 
entropy. If the substance has its condition represented by/, 
it will have a different entropy ; but for any change represented 
by a portion of the line bb^ , as ff^ , the entropy will be constant. 
Just as a change involving the passage from one isothermal to 
another requires a definite change of temperature, so a change 
involving the passage from one adiabatic to another involves a 
definite change of entropy. Thus a passage from e to f involves 
the same change of entropy as a change from c^ to/, ; again, 
the path from e to / is indifferent, and has purposely been rep- 
resented as irregular. 

That the passage from one adiabatic to another under dif- 
ferent circumstances may involve different changes of volume 
and pressure, external work, etc., does not affect the statement 
concerning the entropy. 

An expression for the entropy, as for the different thermal 
capacities, can be found in some cases. Entropy will be repre- 
sented by <p. It is a property of a body similar to specific 
volume, specific heat, and latent heat of expansion, but most 
nearly akin to temperature. It depends on the state of the 
body and not on the method of the change. 



CHAPTER III. 

SECOND LAW OF THERMODYNAMICS. 

Heat Engines are engines by which heat is transformed 
into work. All actual engines used as motors go through con- 
tinuous cycles of operations, which periodically return things 
to the original conditions. All heat-engines are similar, in that 
they receive heat from some source^ transform part of it into 
work, and deliver the remainder (minus certain losses) to a 
refrigerator. 

The source and refrigerator of a condensing steam-engine 
are the furnace and the condenser. 'The boiler is properly con- 
sidered as a part of the engine, and receives heat from the 
source. 

Carnot's Engine. — It is convenient to discuss a simple 
ideal engine, first described- by Carnot ; though, from a defect 
in the theory of heat then accepted, his description was 
erroneous. 

Let P of Fig. 10 represent a cylinder with non-conducting 
walls, in which is fitted a piston, also of non-conducting mate- 
rial, and moving without friction ; on 
the other hand, the bottom of the 
cylinder is supposed to be of a material 
that is a perfect conductor, and which 
^ I has a zero thermal capacity. There is 
a non-conductinff stand C on which the 

Fig. io. ^ 

cylinder can be placed while adiabatic 
changes take place. The source of heat A at a. temperature / 
is supposed to be so maintained that in operations during which 
the cylinder is placed on it, and draws heat from it, the tem^ 
perature is unchanged. The refrigerator B at the temperature 
t in like manner can withdraw heat from the cylinder when it 
is placed on it, at a constant temperature. 

19 



20 THERMODYNAMICS OF THE STEAM-ENGINE, 

Let there be a unit of weight (for example, one pound) of 
a certain substance in the cyHnder at the temperature / of the 
source of heat. Place the cylinder on the source of heat A 
(Fig. lo), and let the substance expand at the constant tem- 
perature /, receiving heat from the source A. 

If the first condition of the substance be 
represented hy A (Fig. ii), then the second 
will be represented by B, and AB will be an 
isothermal. If Ea and Eb are the intrinsic 
energies at A and B, and if Wab , represented 
by the area aABd, be the external work, the 
heat received from A will be 




Fig. II. 



Q = A{E,^E^+W^,), 

Now place the cylinder on the stand C (Fig. lo), and let 
the substance expand adiabatically until the temperature is re- 
duced to /j , that of the refrigerator, the change being repre- 
sented by the adiabatic BC (Fig. ii). If E^ is the intrinsic 
energy at Cy then, since no heat passes into or out of the cylinder, 

o:=A{Ec-E,+ W,,), 

where W^c is- the external work represented by the area bBCc. 
Place the cylinder on the refrigerator B, and compress the sub- 
stance till it passes through the change represented by CDy 
yielding heat to the refrigerator so that the temperature remains 
constant. If Ed is the intrinsic energy at D^ then 

is the heat yielded to the refrigerator, and W^^, represented by 
the area cCDd, is the external work, which has a minus sign 
since it is done on the substances. 

The point D is determined by drawing an adiabatic from A 
to intersect an isothermal through C. The process is com- 
pleted by compressing the substance while the cylinder is on 
the stand C (Fig. lo) till temperature rises to /, the change 



SECOND LAW OF THERMODYNAMICS. 21 

being represented by the adiabatic DA. Since there is no 
transfer of heat, 

Adding together the several equations, member to member, 

or, if W be the resulting work represented by the area ABCD, 
then 

Q-Q, = AW', 

that is, the difference between the heat received and the heat 
delivered to the refrigerator is the heat transformed into work. 

Carnot, in his description of the engine, gives instruction to 
compress the substance during the third operation, and while 
in connection with the refrigerator, till all the heat received 
from the source of heat is yielded, and then to complete the 
cycle by an adiabatic compression. The caloric theory of heat, 
assuming it to be a substance, required such a statement, and 
Carnot compared the difference of temperature to a difference 
of head of water in hydraulics. In the description now common 
the operation of the engine corresponds to the first law of 
thermodynamics. 

A Reversible Engine is one that may run either in the 
usual manner, transforming heat into work, or reversed, describ- 
ing the same cycle in the opposite direction, and transforming 
work into heat. 

A Reversible Cycle is the cycle of a reversible engine. 

Carnot's engine is reversible, the reversed cycle being 
ADCBA (Fig. ii), during which work is done by the engine on 
the working substance. The engine then draws from the 
refrigerator a certain quantity of heat, it transforms a certain 
quantity of work into heat, and delivers the sum of both to the 
source of heat. 



22 



THERMODYNAMICS OF THE STEAM-ENGINE. 




A Closed Cycle is any cycle in which the final state is the 
same as the initial state. Fig. 12 represents 
such a cycle made up of four curves of any 
nature whatever. If the four curves are of two 
species only, as in the diagram representing the 
■ cycle of Carnot's engine, the cycle is said to be 
simple. In general, we shall have for a cycle 
like that of Fig. 12, 



Fig. 12. 



m 



cd 



m.). 



P A 

c 


B 


-5' 


^ 




V 



Fig. 




A closed curve of any form may be consid- 
ered to be the general form of a closed cycle ; 
as that in Fig. 13. For such a cycle we have 

/ dQ = A j dW, which is one more way of 

stating the first law of thermodynamics. 

It may make this last clearer to con- 
sider the cycle of Fig. 14, composed of the 
isothermals AB, CD, and EG, and the 
adiabatics BCy DE, and GA. The cycle 
may be divided by drawing the curve 
through from C to F. It is indifferent 
whether the path followed be ABCDEGA 
or ABCFCDEGA or, again, ABCFGA + CDEFC. 

Again, an irregular figure may be imagined to be cut into 

elementary areas by isothermals and adia- 

batic lines, as in Fig. 15. The summation 

of the areas will give the entire area, and 

the summation of the works represented 

by these will give the entire work repre- 

' sented by the entire area. 

Fig. 15. The Efficiency of an engine is the 

ratio of the heat changed into work to the entire heat applied ; 

so that if it be represented by 7/, 



Fig. 14. 




7 = 






(29) 



SECOND LAW OF THERMODYNAMICS. 23 

Carnot enunciated a principle which may be stated as 
follows : 

Carnot's Principle. — Of all engines working betiveen the 
same source of heat and the same refrigerator^ a reversible engine 
gives the maximum efficiency. 

For, suppose there are two engines, one A, of any kind 
whatever, and one R^ which is reversible, and, for simplicity, 
let each take the same quantity of heat Q from the source of 
heat per unit of time while running direct. The engine R, if 
reversed, will deliver the same quantity Q of heat per unit of 
time to the source. Now, if the efficiency of A is greater than 
that of R, that is, if 

-Q— > —Q-, or Wa > Wr, 

then A, coupled with R, will be able to run R reversed, and at 
the same time produce available work equal to Wa — Wy, 

This surplus work can come from the refrigerator only, since 
the heat taken from the source of heat, and the heat returned 
to it, in a unit of time are equal. But experience and experi- 
ment show that work cannot be so done. Moreover, if it be 
admitted that surplus work can be done at the expense of the 
refrigerator, the admission involves the ultimate conclusion that 
by such a process all the heat might be abstracted from the 
refrigerator. In general, the efficiency of a non-reversible 
engine is less than that of a reversible engine. But there is no 
fundamental reason why it may not approach the efficiency of 
a reversible engine, or become equal to it. 

The Second Law of Thermodynamics is a formal state- 
ment of Carnot's principle. It is variously stated, but each 
statement involves the same principle, which may be considered 
to be an experimental law. 

(i) All reversible eitgiites, working between the same source of 
heat and refrigerator^ have the same efficiency; i.e., the efficiency 
is independent of the working material. 

(2) A self-acting machine cannot convey heat from one body to 



24 THERMODYNAMICS OF THE STEAM-ENGINE. 

another at a higher temperature. This is almost equivalent to 
the.convention, that of two bodies, the one to which heat passes 
by conduction or radiation has the lower temperature. 

Carnot's Function. — Taking Carnot's principle, that the 
efficiency of a reversible engine is independent of the working 
substance, we thereby eliminate from the expression for the 
efficiency the variables p and v^ the specific pressure and the 
specific volume, since they are properties of the working sub- 
stance. The efficiency, therefore, depends only on the tem- 
perature of the source of heat, and the difference between that 
temperature and the temperature of the refrigerator. This 
statement, in the form of an equation, is 



AW 0—0' 

-Q- = ^-Q^=F{t,t-t% . . . (30) 



in which Q is the heat received, and Q' that rejected by the 
engine, and t and f are the temperatures of the source of heat 
and of the refrigerator, on a scale which we have assumed to be 
possible but, as yet, undetermined. 

If the temperature of the refrigerator approaches near that 
of the source of heat, Q — Q! and t — t' become AQ and At^ 
and at the limit dQ and dt, so that 



'^ = F{t,dt) (31) 



But dt is itself a function of /, so that at the limit the effi- 
ciency depends on t only. 

Multiplying and dividing by dt, 



dQ F(i,dt) 
Q - dt ^^^ 



SECOND LAW OF THERMODYNAMICS. 2$ 

and considering that the coefficient of d^ is a function of /only, 
equation (31) becomes 

^=Aiy( (32) 

/ (t) is called Carnot's function, and is represented by/<; its 
form will depend on the thermometric scale adopted. Had 
any scale like that of the mercurial or air thermometer been 
adopted, it would now be necessary to investigate the form of 
the function, which would be more or less complicated. 

Equation (32) is commonly written 

-^ = Mdl. (33) 

Absolute Scale of Temperature. — A scale of temperature 
may now be defined by making ^^z~ so that 

dQ dt 



Q ~T' 



(34) 



the large T being used instead of t to avoid confusion with the 
common scales. The scale depends on the efficiency of the 
reversible engine, and consequently does not depend on the 
property of any substance. Since the reversible engine is 
purely ideal, the absolute scale is also ideal ; but the corre- 
spondence between it and the scale of the air thermometer, with 
which it agrees very closely, can and has been determined by 
indirect methods. The scale proposed is justified by the sim- 
plicity it introduces into thermodynamic equations, and involves 
no inconsistency. 

The method of defining temperature just stated was first 
proposed by Sir William Thomson ; and the thermometric scale 
resulting is sometimes called Thomson's absolute scale. He also 
gives a graphical representation of the scale, which may betaken 
to be the equivalent of the work establishing Carnot's function. 




26 THERMODYNAMICS OF THE STEAM-ENGINE, 

In Fig. 1 6, let ak and bi be two adiabatic lines, and let 
the substance have its condition represented by the point a. 

Through a and d draw iso- 
thermal lines, then the dia- 
gram «/^^<3f represents the cycle 
of a simple reversible engine. 
Draw the isothermal line fe^ 
so that the area dcef shall be 
equal to abcd\ then the dia- 
. gram </^^/ represents the cycle 
^'^- ^^- of a reversible engine, doing 

the same amount of work per stroke as that engine whose cycle 
is represented hy abcd\ and the difference between the heat 
drawn from the source and delivered to the refrigerator, ?>., the 
heat transformed into work, is the same. The refrigerator of 
the first engine might serve for the source of heat for the 
second. 

Suppose that a series of equal areas were cut off by isother- 
mal lines, disfegh, hgik, etc., and suppose there were a series of 
reversible engines corresponding ; then there would be a series 
of sources of heat of determinate temperatures, which might 
be chosen to establish a thermometric scale. In order to have 
the scale correspond with those of ordinary thermometers, one 
of the sources of heat should be at the temperature of boiling 
water, and one at that of melting ice ; and for the Centigrade scale 
there should be one hundred, and for the Fahrenheit scale one 
hundred and eighty such cycles with the appropriate sources of 
heat, between boiling and freezing point. To establish the ab- 
solute zero of the scale the series must be imagined to be con- 
tinued till the area included between an isothermal and the two 
adiabatics, continued indefinitely, shall not be greater than one 
of the equal areas. 

The absolute zero thus determined is very nearly identical 
with that of the air thermometer ; and for all engineering pur- 
poses one may be used for the other. 

Scale of Entropy. — It is convenient to take the areas of 
Fig. 1 6 to represent 778 foot-pounds when the Fahrenheit scale 



SECOND LAW OF THERMODYNAMICS, 2^ 

is used, that being the equivalent of one thermal unit. Sup- 
pose further that a second adiabaticbe drawn through ^W^V^, 
making the area bb'c'c equal to those of the first series ; then the 
points ^, b^ b\ b'\ etc., if a series of adiabatics be drawn, repre- 
sent the conditions of the working substance after the succes- 
sive addition of t units of heat at constant temperature t. The 
adiabatics may be numbered 0, -}~ i> + 2, etc., to 4*' . 

Each one of the areas included between a pair of isothermals 
and a pair of adiabatics will represent the mechanical equivalent 
of one thermal unit, provided abed be chosen as directed above. 
The proof may be given in the following manner: The two 
areas, dcef diXvA bb'c'c^ are equal to abed by construction. The 
two engines working on the cycles abed and bb' e' e each draw 
the same quantity of heat from the source and reject the same 
quantity to the refrigerator ; for they transform the same 
quantity of heat into work per stroke, and, working between 
the same temperatures, they have the same efficiency. The 
engines working on the cycles deef 2sv^ ee' e' e consequently re- 
ceive the same amount of heat per stroke from their sources of 
heat ; and, since they work between the same temperatures, 
they must transform the same amount of heat into work, or 
what is the same thing, the area ee' e' e is equal to deef\ and 
further, all four areas are equal. In the same way the proof 
may be extended to all areas laid off in a similar method. 

A perfect engine working between the isothermals T and T' 
and the adiabatics and 0' will change into work per stroke 
the heat 



(T-T'){<t>'-<p)^AW^Q-Q:, . . (35) 



in which equation is the initial entropy of the working sub- 
stance, and 0' — is the change of entropy from one adiabatic 
to the other. 

Suppose that T' becomes zero, and that (f>' — becomes 
^0, then 



28 



THERMODYNAMICS OF THE STEAM-ENGINE, 



T(l>d=dQ, 

dQ 
T' 



d(j) 



(36) 
(37) 



Efficiency of Reversible Engines.~The efficiency of a 
reversible engine given by equation (29) may be written 



AW Q-Q 



Q 



Q 



(38) 



But the integration of the equation (34) between limits gives 
log. - = loge~. 




T- T 
T • 



(39) 



This equation may also be derived by 



Fig. 



graphical method used in discussing 
absolute temperature. In Fig. 17 
let ABCD be the cycle of a re- 
versible engine working between 
the temperatures T and T' and 
the entropies and 
T' ^ 0^ Let intermediate 

isothermal and adia- 
batic lines be drawn 
dividing the cycle into quadrilaterals each one of which rep- 
resents 778 foot-pounds, or one thermal unit ; then it is appar- 
ent that the number of these quadrilaterals in the cycle, and 
the number of thermal units changed into work, is 

(r-r')(0'-0). 

Similarly, the total heat absorbed during the operation 
represented by AB is 

TW - 0). 



SECOND LAW OF THERMODYNAMICS. 29 

Consequently the efficiency is 

AW {T- T'){(f)' - cp) T-T 



V = 



Q - r(0'-0) 



Alternative Method. — The method of developing the idea 
of temperature from the second law has for an advantage the 
fact that the difficulty of giving an adequate physical defini- 
tion is made prominent. Some writers, Zeuner, Verdet, and 
others, prefer, however, to avoid the difficulty by delaying 
the discussion of temperature ; and of the general equations (5), 
(6), and (7), employ only the latter, 

dQ — ndp -\- odv. 

Equation (23) may be written '' 

which, combined with the equation above, gives 



d'^E 



n — 


fdE\ 
\ dp). 


Differentiating 


,r 


ldn\ 


['(-11 


\dvl- 


\ ^^ 


f^^U 


(Af) ^ 

\dvip 



dpdv' 



_ d'E 
^pK~\ dp J v~^ ~ dvdp^ 

But E depends on the state only, and dE is an exact differ- 
ential ; 

d'^E d'E 



dp dv dv dp 



30 THERMODYNAMICS OF THE STEAM-ENGINE. 

and by subtraction the preceding equations give 



(|).-(£)r' ^^°^ 



Now if dQ were an exact differential, so that it could be 
integrated directly, as would be the case if Q depended on the 
initial and final states only, we should then have 

dp dv dvdp^ 
which may be written 




Performing this operation on equation (7) would give, in 
such case, 



ldo\ _ Id7i\ 
\di)i,, ~ \dvK 



ipl. 

A comparison of this last equation with the true equation 
(40) shows that dQ is not an exact differential, and that equa- 
tion (7) cannot be integrated directly. 

Suppose now that -^ is an integrating factor, such that 



-^^.-dp^^dv 



may be integrated directly. The adiabatic equations 

=: const., (p' = const., 0'^ = const., etc.. 



SECOND LAW OF THERMODYNAMICS. 3 1 

represent a series of adiabatic lines, and in like manner the 
equations 

-r. = const., -^7 = const., -^ = const., etc., 

may represent a series of thermal lines. 

In Fig. 1 8 let the cycle ABCD be com- 
posed of the adiabatic lines AD and CD, and 
the lines AB and CD represented by the 
equations 




I , I 

-^ = const, and ^v = const. 

Fig. i8. O O 

A reversible engine, receiving the heat Q per stroke, and 
rejecting the heat Q , will have the efficiency 

Q-Q AW 
'' = ^~ = ^- 

But -rr is an exact differential depending on the state only, 

so that for the entire cycle 

dQ 



J s ~ 



s 

Now, during the operations represented by the adiabatics 
AD and EC no heat is transmitted, and during the operations 

represented by the lines AB and CD, -^ is constant ; conse- 
quently the integration for the cycle gives 



Q _Q 
S S' 

Q-Q S-S' 



S S'~°' 



Q 



(41) 



That is, the efficiency of an engine working on such a cycle 
depends on 5 and S\ and on nothing else. 



32 THERMODYNAMICS OF THE STEAM-ENGINE. 

Thus far temperature has not been brought into the dis- 
cussion, and it may be defined as seems fit. Let the absolute 
temperature be defined by the equation 

then equation (41) becomes 

Q- Q _ T-T 
Q - T ^ 

so that the absolute temperature depends on the efficiency of 
a reversible engine, as in the preceding discussion involving 
Carnot's function. 

Generalization of Carnot's Principle. — Carnot's princi- 
ple, or the second law of thermodynamics, is sometimes stated 

by making -=i an exact differential, or by writing for a reversi- 
ble cycle 

y = o (42) 



/ 



This is immediately evident from equation (37), since 0, the 
entropy, is a property of the substance and depends on the state 
only. Now in a reversible cycle the substance is in the same 
state at the end as at the beginning of the cycle ; consequently 
if d(p be integrated and the limits used are those at the begin- 
ning and end of the cycle, that is, are identical, the integral 

will be equal to zero. At the same time -^ will give zero for 

its integral between the same limits. This may be represented 
graphically as follows : 

Let ABCDEFGA, Fig. 19, represent a cycle composed of 
isothermals and adiabatics ; then it may be divided by CE into 
two simple cycles. 

For the cycle A B CFG A we have 

Q ~ T ' 



SECOND LAW OF THERMODYNAMICS. 



33 



whence 



Q 



T 



T 



Q 






Q being the heat absorbed at the temperature T along the path 
AB, and Q' the heat rejected at the temperature T' along the 
path FG. 

In like manner for the cycle CDEFC we have 




— -^=o. 



and for the entire figure 



Q 
f 



or 



9L 

T' 



T' 



^y ==0. 



Fig. 19. 



Any cycle composed of isothermals 
and adiabatics may in like manner be divided into cycles, for 
each of which the principle holds, and the summation for the 
whole cycle will give the same result as above.. 

If any area be enclosed by any curve whatever, as in Fig. 20, 
the cycle may be approximately replaced 
by a complex cycle composed of isother- 
mals and adiabatics only, and for such a 
cycle we shall have the same result as for 
the case already discussed. As the curves 
are drawn nearer together the approxi- 
mation will be nearer, and at the limit by 
integration we have 

T 




Fig. 



/ 



= O. 



The two laws of thermodynamics may therefore be expressed 
for closed reversible cycles by the two equations, 

dO 



fdQ = AW, /^-O. 




Fig. 21. 



CHAPTER IV. 

NON-REVERSIBLE PROCESSES. 

Suppose that a body passes from the state represented by 
the point A to the state represented by B, by some process in 

which the pressure exerted by the 
substance, i.e., the specific press- 
ure, is different from the external 
pressure ; then the area aABb 
represents the external work done. 
The usual method for finding 
the change of intrinsic energy for 
a Veversible process is to draw an 
isodynamic Hne AG through the 
point A, and an adiabatic line BG through the point B] the 
area bBGg represents the change of. intrinsic energy, and the 
entire area aABGg represents / times the heat absorbed. If 
the state of the substance corresponding to ^ is a state of 
equilibrium, then the process is equally applicable here. But 
the case is different for any intermediate point, as C \, for it the 
external work is represented by the area aACc, but the change 
of intrinsic energy is not represented by the area cCDd, because 
the body is not supposed to be in equilibrium. If, for example, 
a piston moving in a cylinder is suddenly and forcibly with- 
drawn, the external pressure is less than the specific pressure, 
and the substance is thrown into commotion. Should the 
expansion be arrested at the point C and no heat added or 
abstracted, the body when it arrives at equilibrium will have its 
state represented by the point E, and the increase of intrinsic 
energy will be represented by the area cEFf. The area dDCEFf 
will represent the energy due to the mechanical motion or com- 

34 



NON-REVERSIBLE PROCESSES, 35 

motion of the substance at the state represented by point C of 
the process. 

If a non-reversible process forms a cycle so that the initial 
and final states are identical, then the conservation of energy 
will require that the equation 

fdQ = AW 

\ 
must hold. On the other hand, an investigation of the value of 

-1- will show that the integral for the entire cycle is negative. 

For example, suppose there is a reversible engine working be- 
tween the temperature 2" and T' and the entropies and 0' ; 
then it has been shown that the heat changed into work at each 
stroke is 

(r- T'){(t>' -(!>)-=- Q- Q = AW. 

A non-reversible engine, working between the same tem- 
peratures and taking the same amount of heat per stroke, may 
have a less efficiency because the working substance has at 
times a temperature different from that of the source of heat 
while receiving heat, or from that of the refrigerator while 
yielding heat. In such case 

I 

(2i and (2/» the heat received and the heat rejected, being differ- 
ent from the corresponding amounts for the reversible engine, 
and fFj being less than W. In like manner, if (0' — 0) becomes 
d(t>, then, in general, 

dQ,<{T-T')d4>', 

and should the temperature T' approach zero, then (7*— T') 
will approach 7", and at the limit 

dQ, < Td(t>, 
. dQ, 






<d<p, 



36 THERMODYNAMICS OF THE STEAM-ENGINE, 

or, dropping the subscript, 



/f</^^ 



for a non-reversible cycle, 

But, since the cycle is supposed to be complete, the initial 
and final states of the body are identical; so that, integrating 
with those states as limits. 

fd(p = o. 
Therefore, for a non-reversible cycle, 

/f--^> (43) 

in which N may have any value ; z.e.f it may approach zero. 



CHAPTER V. 

FUNDAMENTAL EQUATIONS. 

Application of the First Law. — Equations (5) and (23) 
give 

dQ = A{dE + dW) = c^t + Idv ; 

or, replacing dWhy pdv, 

A{dE + pdv) ^ c^dt -\- ldv\ 

/. dE^'~dt+(-^^p)dv (44) 

Now E depends on the state of the body only, and not on 
the method of changing from one condition to another ; that 
is, dE is an exact differential, and consequently 

d'E d'E 



dt dv dv dt ' 
which may be written 



f ). = ] K' 



dE\ 

dvit 
dt 



in which the partial differential coefficients are those of the 
equation 

Comparing with equation (44), it appears that 

37 



38 THERMODYNAMICS OF THE STEAM-ENGINE, 

and that consequently 

dvKAJi ~ d'AA ~ ^y, ' 



•'• ALWd^, \dvlj~\dl 



(45) 



The combination of equation (23), which expresses the first 
law of thermodynamics, with equation (5), is the application of 
the first law to that equation, and equation (45) is the relation 
between the latent heat of expansion and the specific heat at 
constant volume which must exist if that law be true. 

In a similar manner the first law may be applied to equa- 
tion (6), as follows : 

dQ = A{dE -\- pdv) = Cpdt + mdp. 
Substituting the value of dv from the equation 

••• '^^ = Li - Adt)M + b - A^) J^^- 



But 



d'E _ d'E 
dtdp dpdt 



I idci 
A 



dVcp_ 
dp LA 



^tf)J. 



_ d Fm fdv \ "] 

~ JLa ~ AdplJ, 



•«f) 



\dp)t \dt)p A "^P 




But 



FUNDAMENTAL EQUATIONS, 39 



d'v d'v 



dp dt dt dp^ 

- :^[(t),- (SXfl <*^ 

which is the relation between the thermal capacity m and the 
specific heat at constant pressure developed by the appHcation 
of the first law to equation (6). 

Again, the same law may be applied to the equation (7). 

dQ — A{dE -\- pdv) = ndp + odv\ 

/. dE='^dp-\-[^-p^dv (47) 



Since 



d^E d'E 



dp dv dv dp'' 

fdn\ I I do \ 

[d^j. ~ A\dp)^ 



i; 



I Ffdo \ fdn \ 

~AL.\dp)^ ~ \dv]pA 



= 1 (48) 



Application of the Second Law. — The second law of 

dQ 
thermodynamics is expressed by making -^ an exact differen- 
tial. Applying this to equation (5) in the same way as was 
done with the first law, 

-jT = -rpdt -\- -^dv . 



40 THERMODYMAMICS OF THE STEAM-ENGINE. 

But 



./f ./- 



dt dv dv dt ' 



i'r), - dAT): 



rdA 



rrA -I 
. T\dv), - r ' 

"*• y.~ ttl = r- • • • • • (49) 



the relation between / and c^ developed by the application of 
the second law to equation (5). 

Applying to equation (6), we have 



dQ cp , ^ , 



P 



^(Cp\ _ d lm\ 
dp\f)t~dt^~~ 

ldm\ 
T\dp],- T' 

ldcp\ {dm\ m , , 

\dp)r\-dt]r-T (50) 



FUNDAMENTAL EQUATIONS. 4I 

Again, applying to equation (7), 

— - — -jrdp + ^dv, 
d in\ ^ ( ^\ 

^ldn\ (dt\ ^[do\ idt\ 

First and Second Laws Combined. — The result of ap- 
plying both the first and second laws of thermodynamics simul- 
taneously to the fundamental equations is deduced by uniting 
the equations obtained by applying each separately. 

For the equation (5), in terms of c^ and /, the comparison 
of equations (45) and (49) gives 



dp\ I / 



(52) 



For equation (6), equations (46) and (50) give 

Ul^-AT (53) 

Also for equation (7), equations (48) and (51) give 



42 THERMODYNAMICS OF THE STEAM-ENGINE. 

Or, substituting the values of n and o from equations (17) and 

"-'■ = ^^)0r\ •<") 

Zeuner's Equations. — In his Mechanische Wdrmetheorie , 
Zeuner employs the alternative method, so far as to deduce 
equation (42). Then, instead of assuming that vS is the abso- 
lute temperature, or giving such a definition of temperature, he 
assumes that the similarity of the thermodynamic equations to 
certain gravitation equations indicates an essential similarity, 
and thereby avoids the second law of thermodynamics. With- 
out discussing his method, there appears no reason why it 
might not be applied to deduce equations of the same form as 
those given here. He, however, gives equations of a different 
form which may readily be deduced from our own, and which 
it may be convenient to write down here. Comparing equation 
(47) with 



^^=6i).*+sa-. 



it is evident that 



o (dE\ , 



forms which were deduced in the alternative method of the 
second law of thermodynamics. These Zeuner writes : 



-= o, 



-=/+(£)/ 



FUNDAMENTAL EQUATIONS. 43 

Solving equation (54) for and for n, 



AT 



= 






-^--"©. 



wi 



Substituting the values successively in equation (7), we have 
the following : 

\dpK 



But 



dQ= i^^ indt -^ ATdvY, 
\dv). 



'dv 



dQ-^ {Jpj [odt-ATdp]. 



44 THERMODYNAMICS OF THE STEAM-ENGINE. 

Zeuner deduces, for his fundamental equations, 

dQ = A{Xdp + Ydv) ; 



\dp) 



dQ^ ^ 



\dv] 



which may readily be deduced from the equations above. 



CHAPTER VI. 

PERFECT GASES. 

The characteristic equation of a gas is the algebraic ex- 
pression of the combined laws of Boyle and Gay Lussac. 

pv=p,v,{i-\-at)=p,v,a\-^t)) .... (56) 

pv = RT- (57) 

/o and % being the specific pressure and specific volume at freez- 
ing, and oc their coefficient of dilatation at constant pressure. 

Coefficient of Dilatation. — Regnault^ gives for the dilata- 
tion from freezing to boiling point, at Paris, the results : 

Hydrogen, 0.3667 

Atmospheric air, 0.3665 

Nitrogen, 0.3668 

Carbonic acid, 0.3688 

In works on thermodynamics it has been commonly assumed 
that the coefficient of dilatation for air may be used for all 
gases, and at all temperatures and pressures, and that, conse- 
quently, on the Centigrade scale, a is 0.003665, or very nearly 
-gJ-3. Professor Holman f suggests that as the pressure ap- 
proaches zero, the coefficient of dilatation of all gases 
approaches 

I 

a = : , 

2737 

* Memoires de I'lnstitut de France, tome xxi. 

f Lecture Notes on Heat, Mass. Inst. Technology, 

45 



46 THERMODYNAMICS OF THE STEAM-ENGINE. 

which agrees with thermodynamic investigations relating to the 
absolute zero of temperature. On the Fahrenheit scale, 



a = 



492.7 



Specific Volume. — This quantity is determined from the 
density, which is given for several gases in the following table, 
at freezing point and at atmospheric pressure, as determined 
by Regnault. 

Weight in grams of one liter : 

Atmospheric air, 1-293 187 

Nitrogen, . 1.256 167 

Oxygen, 1.429 802 

Hydrogen, 0.089 57^ 

Carbonic acid, 1-977 414 

The specific volumes are as follows. Volumes in cubic 
meters of one kilogram, at Paris, latitude 48° 50' 14'' ; elevation, 
60 meters : 

Atmospheric air, 0.773 2834 

Nitrogen, . 0.796 0724 

Oxygen, ....... 0.699 3974 

Hydrogen, 11-163 46 

Carbonic acid, 0.505 7109 

The specific volumes, reduced to the latitude of 45° at sea 
level, are given in the next table. 

Volumes in cubic meters of one kilogram, at 45° of latitude : 

Atmospheric air, 0.773 5327 

Nitrogen, . . . .' . . . 0.796 3291 

Oxygen, 0.699 6231 

Hydrogen, 1 1. 167 05 

Carbonic acid, O.505 8741 



PERFECT GASES. 47 

The reduction for the change of the acceleration due to 
gravity is made by the equation * 

g — 980.6056 — 2.5028 cos 2\ — 0.000003-^, . (58) 

in which g is the acceleration in centimeters, 'K. is the latitude, 
and h is the elevation above the sea in centimeters. One kilo- 
gram f is equivalent to 2.20462125 pounds; and one meter, as 
determined by Professor Rogers, if is equivalent to 39.3702 
inches, from which the specific volume in English units may be 
determined. 

Volumes in cubic feet of one pound at 45° of latitude; 

Atmospheric air, 12.3909 

Nitrogen, 12.7561 

Oxygen, 11.2070 

Hydrogen, 178.881 

Carbonic acid, 8.10324 

Specific Pressure. — The weight of one liter of mercury, 
determined by Regnault, is 13.5959 kilograms; consequently 
the pressure of one atmosphere, or 760 mm., of mercury on one 
square meter is 

10333 kilograms. 

Using the values given above for the kilogram and meter 
we have, for the English system, 

14.6967 pounds per square inch, 
2116.32 pounds per square foot. 

Value oi R. — Taking the value of /„ , v^ , and a, at freezing 
point and under the pressure of 760 mm. of mercury, we have 
for air, 

* Everett's Units and Phys. Const. 

f Miller, Phil. Transactions, cxlvi, 1856. 

X Pro. Am. Acad, of Arts and Sci., 1882-83 \ also additional observations. 



48 THERMODYNAMICS OF THE STEAM-ENGINE. 

French units, 7e^ ^^333X0.77353 ^ ^ 

273.7 ^ 

^ ,. , . ^ 2116.S X 12.SQI ,^ , 

English units, R — ^^ — 53.22. . (60) 

The value of R for other gases may be determined in a hke 
manner. 

Specific Heat at Constant Pressure. — The specific heat 
for true gases is very nearly constant, and may be considered 
to be so for thermodynamic equations. Regnault gives for 
the mean values for specific heat at constant pressure the fol- 
lowing results : 

Atmospheric air, 0-2375 

Nitrogen, 0.2438 

Oxygen, 0.2175 

Hydrogen, ......... 3.409 

Application of the Two Laws of Thermodynamics. — 

The result of applying the two laws of thermodynamics to 
equation (7) is given by equation (55), 

Differentiating the characteristic equation (57) for a gas, 
idv\ _ R idp\ _ R 

which, substituted in equation (55), give 

Cp-c^^AR (61) 

Specific Heat at Constant Volume. — The specific heat 
at constant volume has not been determined directly. It is 



PERFECT GASES. 49 

evident from equation (61) that the assumption of the charac- 
teristic equation (57), and the assumption that Cj, is constant, 
make c^ also constant. It will be seen subsequently that the 
ratio of the specific heats may be determined experimentally. 
The ratio is commonly taken to be 



Cp 

T-^'^^ 1.405. 



Thermal Capacities. — Substituting the values of the par- 
tial differential coefficients as deduced from equation (57), in 
equations (ii), (15), (17), and (18), we have, for the values of the 
thermal capacities for gases, 

/ T 

^ = ;^fo-^-) ^-fe-^e'); . . . • (62) 



m = -^{cp- c,) = - — {cp-c^)', , . . (63) 



V T 






Combining these four equations with equation (57) gives 

l=Ap', {66) 

m — — Av ; i^f) 

n = Av-^^—] ...... (68) 

c^ — c„ 



o=Ap^-^~ (69) 



c,. - f „ 



50 THERMODYNAMICS OF THE STEAM-ENGINE. 

General Equations. — The values of the thermal capacities 
given by equations (62), (63), (64), and (65), substituted in equa- 
tions (5), (6), and (7), give 



T 
dQ = c^dt + {cp — c^)—dv\, . , . (70) 



T 

dQ — Cpdt + {c^ — Cp)--dp\ , . . . (71) 



T T 

dQ — c^-- dp -\- Cp— dv. . . . . . (72) 

Just as the first law of thermodynamics was applied to the 
general equations (5), (6), and (7), by equating them to equation 
(23), so the first law may be applied to equations (70), (71), and 
(72) in the same manner. For example, the application of the 
first law to equation (70) gives 



T 

dQ — A [dE -\-pdi) = c^dt -\- {cp — c^ ~dv ; 



dE^-^dt ^ \^~{cp-c^)---p\dv) 

Cp-c.^Av{§)j, 
Cp— c^ — AR. 



PERFECT GASES, , 5 1 

The application of the same law to each of the other two 
equations, (71) and (72), gives the same result. The fact that 
the result is the same as that resulting from the application of 
both laws of thermodynamics indicates that the characteristic 
equation for gases implies the second law. An attempt to apply 
the second law to equations (70), (71), and (72) in the usual 
manner gives in each case zero equal to zero, which reaffirms 
the preceding statements in another form. 

Isothermal Lines. — The equation to the isothermal line 
for gas is obtained by making T constant in the general equa- 
tion, which gives the equation representing Boyle's law : 

/^^=A% = const., (73) 

which is the equation to a rectangular hyperbola. 

The heat absorbed during an isothermal change is obtained 
by integrating one of the general equations (70), (71), or (72) 
with T assumed to be constant, so that dt becomes zero. 

Equation (70) gives 

dv 



Q = icp-c:)T£; -l 



■ •■ Q = {c^-c.)riog,~'; (74) 

or, substituting for the value of Cp — c^ from equation (68), 

G = ^i?riog,^' = ^A^jog,^'. . . (75) 

In like manner equation (71) gives 

Q = {c,-c,)T\o^,^ ; {^6) 

Pa 

.-. Q = ART\og/^ = Ap,v, log, -|?_ ; . {77) 



52 THERMODYNAMICS OF THE STEAM-ENGINE. 

which equations can be deduced from the preceding by substi- 
tuting for — from the characteristic equation. 
To find the work done, the equation 

W= r^ pdv 

may be used after substituting for / from the characteristic 
equation, whence 



W 



•''' dv , v^ 



A% / - =A%log,-. . . . (78) 




A comparison of equations (75) and (78) shows that all the 
heat absorbed is changed into external work ; consequently the 
intrinsic energy remains unchanged during the operation. 

The area contained between the axis (9 F", 
Fig. 22, the ordinate ab^ and the isothermal 
line aoL extended without limit, is 

00 
W^p.v, log.— = 00. 

^i^- 22- This may also be seen from the consid- 

eration that if heat be continually applied, and all changed 
into work, there will be a limitless supply of work. 

Isoenergic or Isodynamic Lines. — In the discussion 
of isothermal lines it appears that all the heat received is 
changed into work ; consequently the intrinsic energy remains 
constant during an isothermal change. From which it is appar- 
ent that the isoenergic line is coincident with the isothermal 
line. 

From the importance of the subject, an independent proof 
will be given that ^ is a function of t only. 

dQ=A{dE + pdv)', 

.fl=.(fl,.,+4(f-),+,>. 



PERFECT GASES. 53 

Comparing with equation (71), it is apparent that 



'dE\ 
dvl t 
Again, 



t 



Comparing with equation (72), it is apparent that 

The importance of the proposition that ^ is a function of f 
only, will be apparent in connection with the comparison of the 
scale of the air thermometer with the thermodynamic scale. 

Adiabatic Lines. — During an adiabatic change, for exam- 
ple, the expansion of a gas in a non-conducting cylinder, heat 
is not communicated to, nor abstracted from, the gas ; conse- 
quently dQ in equations (70), (71), and (72) becomes zero. 

From equation (72), 

o =z dQ = ^-^ vdp ^^-^ pdv ; 
Cp dv __ dp 

Cv V P 



■-(ir=-(f> 



54 THERMODYNAMICS OF THE STEAM-ENGINE. 

The ratio — of the specific heats may be represented by /c, 
and the above equation may be written 



©■ 



%■■ w 



.•. ^"Z =z '^^//>„ = const (80) 

From equations (70) and (71), 

^^''-i r=:z;/-^ 7; = const, « . . . (81) 



K 



7> " = 7;// - ^ = const. ; .... (82) 

or these last two equations may be deduced from equation (80) 
by substituting for p or for v from the characteristic equation. 
To find the external work, the equation 

W=fpdv 

may be used after substituting for/ from equation (79) or (80). 

W= pdv=V^''p^ rz:— ZLJ_ ; 

■■■«'=;ff;l--(r'l <*3) 

In Fig. 23 the area between the axis OV, 
I the ordinate ba, and the adiabatic line aa ex- 

\a tended without limit becomes 



Fig. 23. '^ ^ 

and not infinity, as is the case with the isothermal line. 



PERFECT GASES. 55 

Intrinsic Energy. — Since the external work is done at the 
expense of the intrinsic energy, the work obtainable by an in- 
finite expansion cannot be greater than the intrinsic energy. 
If it be admitted that when the volume becomes infinity and 
the pressure and temperature become zero, the intrinsic energy 
becomes zero, then we shall have 



E,=.W, = P^. . . . . . . (84) 



which gives a method of calculating the intrinsic energy. 

Though such a method of calculating the intrinsic energy 
is subject to an error, from the fact that at zero temperature 
and pressure the intrinsic energy is not zero, the error is con- 
stant for all values of intrinsic energy, and disappears when 
differences are taken. 

Entropy. — From equation (71) we have 

dQ_ dt dp 

-^ — ^^ -^ -f- (^^z, — <:/ j —- , 

which, for a reversible cycle, is equal to the differential of the 
entropy. Consequently we have, on integrating between limits, 

T p 

- 00 = ^/ log,-:^ -f (C^ ~ C^) log,— . . . . (85) 

This gives a method of calculating the increase of entropy 
above that at a certain state ; for example, above that at freez- 
ing-point and under normal atmospheric pressure. 

Similar expressions maybe deduced from equations (70) and 

(72). 

Carnot's Cycle. — It has already been shown that the char- 
acteristic equation for a gas implies the second law of ther- 
modynamics, but it can be shown in another and more direct 
way by aid of Carnot's cycle. The demonstration is frequently 
given in elementary works, and may be useful as an exercise. 




56 THERMODYNAMICS OF THE STEAM-ENGINE. 

The equation to the isothermal line for a gas was deduced 
from the characteristic equation by making 
T a constant, and the equation to the adia- 
batic line was deduced from equation (72) by- 
making dQ equal to zero ; in all of which no 
direct reference was made to the second law 
of thermodynamics, or the efficiency of a 
reversible engine. Let us now consider the 

Fig. 24. =* 

cycle of Carnot s engine for a perfect gas. 
We shall have, as in the general case, that the area of ABCDA 
(Fig. 24) represents the work done ; that is, 

W=W,t^Wi,-W.^-Wa,. . . . (86) 

Since AB and DC are isothermal lines, 



W^ = J>.v^\og,^, (87) 



f^^.=/^ilog,^; (88) 



and since BC and DA are adiabatic lines 






The last two quantities of work are equal, for we have 



PERFECT GASES. s 57 

because the points a and b are on the same isothermal line ; 
and since a and d are on one adiabatic line, and b and c are on 
another, we have 






T 



Zj being the absolute temperature of the isothermal line AB, 
and J", of DC. 

The last two equations give also 

^_^ . '^ — '^ 

and the characteristic equation gives 

paVa — RT^, pdVd = RT^; 
whence equations (87) and (88) reduce to 



and these values inserted in equation (86) give 

rr=^(7-,-r,)iog.|, 

To calculate the heat received by the working substance in 
passing along the isothermal from A to B, we may employ 
equation (65) with the condition that T shall be constant, and 
dt shall be zero. Integration between limits gives 



58 THERMODYNAMICS OF THE STEAM-ENGINE. 

which, by aid of equation (68), may be reduced to 



(2. = ART, log.^ 



Now the efficiency of any engine is 



V 



from which the efficiency of an air-engine, working on Carnot's 
cycle, is 

^ = '^=i-^-^, . . . (89) 

ART.logA ' 



Comparison of the Air Thermometer with the Absolute 
Scale. — In connection with the isodynamic line it was shown 
that the intrinsic energy is a function of the temperature only. 
This conclusion is deduced from the characteristic equation on 
the assumption that the scale of the air thermometer coincides 
with the thermodynamic scale, and affords a delicate method 
of testing the truth of the characteristic equation, and of com- 
paring the two scales. 

The most complete experiments for this purpose were made 
by Joule and Sir William Thomson, who forced air slowly 
through a porous plug in a tube in such a manner that no heat 
was transmitted to or from the air during the process. Also the 
velocity both before and beyond the plug were so small that 
the work due to the change of velocity could be disregarded. 
All the work that would be developed in free expansion from 
the higher to the lower pressure was used in overcoming the 
resistance of friction in the plug and so converted into heat, 



PERFECT GASES. 



59 



and as none of this heat escaped it was retained by the air 
itself, the plug remaining at a constant temperature. It there- 
fore appears that the intrinsic energy remained the same, and 
that a change of temperature indicated a deviation from the 
assumptions of the theory of perfect gases. The change, 
though slight, was measurable, and has been used to establish 
the comparison between the two thermal scales under dis- 
cussion. 

In the discussion of results given by Joule and Thomson * 
in 1854 they give for the absolute temperature of freezing- 
point, 273°. 7 C. As the result of later f experiments they state 
that the cooling for a difference of pressure of 100 inches of 
mercury is represented, on the Centigrade scale, by 



o°.92 



(^^y 



The following table shows the agreement between this state- 
ment and the results of experiment : 

FLOW OF AIR THROUGH POROUS PLUG. 



Temperature. 


Cooling Effect — 


By Experiment. 


By Calculation. 


0° 

7-1 

39-5 

92.8 


0.92 

0.88 

0.75 
0.51 


0.92 
0.87 
0.70 
0.51 



From the work of these experiments Rowland % deduced the 
following comparison of the air thermometer with constant 
volume, with the absolute thermodynamic scale of temperature. 



* Philosophical Transactions, vol. 144, p. 349. 

f Ibid., vol. 152, p. 579. 

ij: Proceedings of the American Academy, vol. xv. (N. S. viii.) p. 75; 1879. 



6o 



THERMODYNAMICS OF THE STEAM-ENGINE. 



REDUCTION OF THE AIR THERMOMETER TO THE 
ABSOLUTE SCALE. 

{Centigrade.^ 



Temperature above Freezing. 








Correction to Air 
Thermometer. 






Air Thermometer. 


Absolute Scale. 




o° 

lO 


9.9972 


— 0.0028 


20 


19.9952 


— 0.0048 


30 


29.9939 


— 0.0061 


40 


39.9933 


— 0.0067 


50 


49.9932 


— 0.0068 


60 


59-9937 


— 0.0063 


70 


69.9946 


— 0.0054 


80 


79-9956 


— 0.0044 


90 


89.9978 


— 0.0022 


100 


100.000 


0. 


200 


200.037 


^ 


-0.037 


300 


300.092 


- 


- 0.092 


400 


400.157 


- 


-0.157 


500 


500.228 


" 


-0.228 



CAB 



Fig. 25. 



Velocity of Sound. — Sound is transmitted through the air 
in spherical waves, but at a distance from the source of sound 
the waves are sensibly plane waves, and 
~Z^ the progress of the wave is the same as 
— that of a plane wave in a straight tube of 
uniform section. Let Fig. 25 represent a 
tube one square meter in section, in which a wave moves with 
a linear velocity ?^o meters per second; that is, a point at a given 
phase of the wave, for example, C at the greatest condensa- 
tion, moves at that velocity. 

Since the wave moves with the velocity u^ , the volume of 
air disturbed in a unit of time is u^ cubic meters. If the 
specific volume in the undisturbed state is v^ , then the weight 
of air disturbed in a second is 



w = mg^ 



^0 



m being the mass of air which has the weight w. 



PERFECT GASES. 6l 

Imagine two planes A and ^ at a small distance apart, which 
also move with the velocity u^ , so that they remain at the same 
phase of the wave. Let the absolute velocities of the air at 
these planes be u^ and u^ ; then the velocities of the air through 
the planes, that is, the velocities relatively to the planes, is, for 
Ay u^ — u^, and for B, u^ — u^ . With v^ and v^ for the specific 
volumes at these planes, the weights that pass through the 
planes A and B per second are 



and 



^0- 


U, 




u. 


— 


u^ u, 


^. 








^. 


^c 


• • 


^1 


= 


u. 


— 


mv,g\ 



Since the phase of that portion of the wave between A and 
B is constant, the weight of the air between them is also con- 
stant, and as much air enters per second as leaves during that 
time. Again : as, on the whole, the air is not transmitted, but 
only compressed and rarefied, the whole air disturbed per 
second must pass through the space between the planes. 
Therefore, 



— mg\ 



u^ — u, = mgiy^ — V,). 

Now, as the mass m enters the space between the planes 
with the absolute velocity u^ , and an equal mass leaves with 
the velocity u^, consequently there is a change of momentum 

m {u, — u^ ; 

and since this cannot come from the mutual action of the par- 
ticles, it must come from the difference of pressures at A and 
B\ thus. 



62 THERMODYNAMICS OF THE STEAM-ENGINE. 

As the planes A and B approach each other, /^ and /j, v^ 
and v^ approach in value, and at the limit 

dp ■= — m'gdv, 

dp .^ I u,^ 

dv ^ gv^ 

the last reduction being obtained by substituting for the value 
of m from the preceding work. Solving for u^ , 

.dp 

The vibrations are so rapid that the changes of state may- 
be assumed to be adiabatic ; consequently equation (72) gives 



= 


dQ^ 




vdp 


^\pdv; 


dp 

dv~ 




V 


m - 


V 



The planes A and B may be taken at any phase of the 
wave ; for example, at the phase where the pressure and volume 
are normal, in which case 

dv v^' 

Substituting in the equation for u^ , we have 

<=^/^^oA- • (90) 

The equation is commonly given in terms of the density, /, 
as follows : 



=\A^^ fei) 



PERFECT GASES. ^l 

Ratio of the Specific Heats. — The velocity of sound from 
direct experiment was found by Moll and Van Beek to be 
332.26 meters per second ; by Regnault to be 330.70 meters per 
second. Kayser found from Kundt's dust figures the wave 
length corresponding to a certain tone, and therefrom deduced 
the velocity of sound, and gives for the velocity 332.50 meters 
per second. The true value must be nearly 332 meters per 
second. Solving equation (94) for /c, and intersecting the 
known values oi p^v^ and ^ for Paris, 



< 332' 

K = 



gv,p, 9.8092 X 0.77328 X 10333 ' 

K = 1.4063. 

Direct experiments to determine k may be made as follows : 
Suppose that a vessel is filled with air at a pressure /j, while 
the pressure of the atmosphere is/^ • Let a communication be 
opened with the atmosphere sufficient to suddenly equalize the 
pressure ; then let it be closed, and let the pressure p^ be ob- 
served after the air has again attained the temperature of the 
atmosphere. If the first operation is sufficiently rapid it may 
be assumed to be adiab^tic, and we may use equation (79), from 
which 

^^logA-logA 

log v^ — log v^ ^^ ^ 

The second operation is at constant volume ; consequently 
the specific volume is the same at the final state as after the 
adiabatic expansion of the first operation. But the initial and 
final temperatures are the same ; consequently 

. • . log ?7„ — log V^ = log p, — log/, , 



64 THERMODYNAMICS OF THE STEAM-ENGINE. 

which, substituted in equation (92), gives 

log A — log A 



log A - log A 



(93) 



The same experiment may be made by rarefying the air in 
the vessel, in which case the sign of the second term changes. 

Rongten "^ employed this method, using a vessel containing 
70 liters, and measuring the pressure with a gauge on the same 
principle as the aneroid barometer. Instead of assuming the 
pressure /„ at the instant of closing the stop-cock to be that of 
the atmosphere, he measured it with the same instrument. A 
mean of ten experiments on air gave 

yc= 14053- 
Again, from equation (68) we have 



C. i_^' 



K = 



10333 X 0.77353 



426.9 X 273.7 X 0.2375 
/c = 1.4046. 

The value of /c already given on page 49 will be used 
throughout our work, i.e., 

K — 1.405. 

Solution of Problems. — The greater part of engineering 
problems involving gases may be solved by the aid of the char- 
acteristic equation 

pv =r RT, 

* Poggendorff' s Annalen, vol. cxlviii. p. 580. 



PERFECT GASES. 65 

or the equivalent equation, 



In the first of these two equations the specific pressure and 
volume to be used for English measures are pounds per square 
foot, and the volume, in cubic feet, of one pound. 

For example^ let it be required to find the volume of 3 pounds 
of air at 60 pounds gauge pressure and at 100° F. Assuming 
a barometric pressure of 14.7 pounds per square inch, 



53.22(4607+ 100) , . , 

V = ^ — ' , ' ' ^ = 2.773 cubic feet 

(14.7 + 60)144 ^^^ 



is the volume of i pound of air under the given conditions, and 
3 pounds will have a volume 

3 X 2.773 = 8.319 cubic feet. 

The second equation has the advantage that any units may 
be used, and that it need not be restricted to one unit of weight. 

For example, let the volume of a given weight of gas, at 
100° C.and at atmospheric pressure, be 2 cubic yards; required 
the volume at 200° C. and at 10 atmospheres. Here . 



loz^ I X 2 



4737 373.7 

473.7 X 2 



V = 



10^3737 ~ ^'^535 cubic yards. 



66 THERMODYNAMICS OF THE STEAM-ENGINE. 



EXAMPLES. 

1. Find the weight of 4 cubic meters of hydrogen at 30° C. 
and under the pressure of 800 mm. of mercury. 

2. Find the volume of 3 pounds of nitrogen at a pressure of 
•45 pounds to the square inch by the gauge, and at 80° F. 

; 3. Find the temperature at which one kilogram of air will 
occupy one cubic meter when at a pressure of 20,000 kilograms 
per square meter. 

4. Find the pressure at which 2 pounds of carbonic acid at 
freezing-point of water will occupy 3 cubic feet. 

5. A gas-receiver having the volume of 3 cubic feet con- 
tains half a pound of oxygen at 70° F. What is the pressure ? 

6. A spherical balloon 20 feet in diameter is to be inhated 
with hydrogen at 60° F. when the barometer stands at 30.2 
inches, so that gas may not be lost on account of expansion 
when it has risen till the barometer stands at 19.6 inches, and 
the temperature falls to 40° F. How many pounds and how 
many cubic feet are to be run in ? 

7. A gas-receiver holds 14 ounces of nitrogen at 20° C. and 
under a pressure of 29.6 inches of mercury. How many will it 
hold at 32° F. and at the normal pressure of 760 mm. ? 

8. Two cubic feet of air expand at 50° F., from a pressure 
of 80 pounds to a pressure of 60 pounds, by the gauge. What 
is the external work ? 

9. What would have been the external work had the air 
expanded adiabatically ? 

10. Find the external work of 2 pounds of air which ex- 
';i:>ands adiabatically until it doubles its volume; the initial 

jjiessure being 100 pounds absolute, and the initial tempera- 
ture 100° F. 

11. Find the external work of one kilogram of hydrogen 
which, starting with the pressure of four atmospheres and with 
the temperature of 500° C, expands till the temperature be- 
comes 30° C. 

12. Find the intrinsic energy of one pound of the several 



PERFECT GASES. 67 

gases for which the proper data are given, under the standard 
pressure of one atmosphere and at freezing-point of water. 

13. A pound of air has the volume 6 cubic feet under the 
pressure of 30 pounds absolute to the square inch. Find the 
intrinsic energy. 

14. In example 13, find the increase of entropy above that 
at atmospheric pressure and at freezing-point. 

15. A kilogram of oxygen at the pressure of 6 atmospheres 
and at 100° C. expands isothermally till it doubles its volume. 
Find the change of entropy. 

16. Suppose a hot-air engine, in which the maximum pres- 
sure is 100 pounds absolute, and the maximum temperature is 
600° F., to work on a Carnot's cycle. Let the initial volume be 2 
cubic feet, let the volume after isothermal expansion be 5 cubic 
feet, and the volume after adiabatic expansion be 8 cubic feet. 
Find the external work of one cycle ; also the horse-power if 
the engine is double-acting and makes 30 revolutions per 
minute. 



CHAPTER VII. 

SATURATED VAPOR. 

Our knowledge of the properties of saturated vapors is de- 
rived mainly from the experiments made by Regnault.* In 
almost all cases the results of the experiments are stated in form 
of empirical equations designed to be used for calculating 
tables ; and since such tables are of great value and importance 
in steam-engineering, it appears advisable to give at some 
length the data on which those equations are based, so as to 
show the limits of their application and their degree of accu- 
racy. In some cases the constants of the equations have been 
recalculated ; notably in the case of the pressure of saturated 
steam, which appeared to be necessary on account of the diver- 
sity of the values given by different authors for the constants 
in the empirical equations used for calculating tables, and on 
account of the discrepancy between the steam tables in , com- 
mon use, especially on the English system of units. 

Pressure of Saturated Vapor. — Regnault's experiments 
on the temperature of saturated vapor consisted essentially in 
taking the temperature of the boiling-point of the vapor under 
varying pressures of the atmosphere, the apparatus being so 
arranged that the pressure could be varied from a small frac- 
tion of an atmosphere to more than twenty atmospheres. The 
temperature was taken with mercurial thermometers, and the 
pressures were measured by a mercury column, and, after the 
necessary corrections were applied and temperatures were re- 
duced to the air thermometer, Regnault selected the results he 
deemed most trustworthy, and plotted a series of points, and 

* Memoires de I'lnstilut de France, etc., tome xxvi. 

68 



SATURATED VAPOR. 



69 



then drew a smooth curve to represent the whole series of ex- 
periments. 

He then selected points on the experimental cur\^e at regu- 
lar inter\'als, and with these points as data he calculated the 
constants of empirical formulae for use in calculating the tabular 
values. The formula selected was of the form 



log/ — aA;- ba"" -f- ^y5« , 



(94) 



in which / is the pressure, and ;/ is the temperature minus the 
constant temperature t^ of the lowest limit of the range of tem- 
perature to which the formula applies ; i,e., 

71 = t- t,. 

Let the points through which the curve represented by the 
equation is to pass be (/„, /„), (/,, /,), (/„ /,), (/„ t^, and (/,, /,), 
so chosen that 

Substituting the five known values of/ and f in equation (94), 
log/, = a-{- ba''-'' +cj3''-'' ; 

iogA = ^+^«^'^"'"^ + ^y5^^''"'°n- • • (95) 

log/3 = a-{-ba'^''-'''^ + cj3'^'^-'''; 
log/, = ^ + ba''''-''^ + cj3*^'' '''\ 

Now subtract each equation, member for member, from the 
one below it, and for convenience let 

log/, -log A =x, etc., a''-'* = m, lS''-'* = n, 

•*• J^o = (^^^ — I ) '^ + (^^ — I ) ^ i " 



y^ = M — in)b -{- {71^ — 7i)c ] 

y^ = {m' - 17t')b -\- {7t' - 7l'')c \ 
y^ = {m' -77l')b + {7l' -7l')c. 



(96) 



70 THERMODYNAMICS OF THE STEAM-ENGINE. 

Solving the several equations for c and equating the values^ 

y^ — {m — i) <^ _ i'l — C^'* — m) b 
n — I n^ — n 

_y^ — {m^ — nf) b ^y^ — {m^ — m^) b , . 

n — n n — n 

Again, solving for b and equating the values and reducing^ 

^jo — y^ ^ i^y—y-. ^ ^^j^^— .Ts 

n — m (n — m)fn {n — m)'m^ ' 
.'. n^ny^ — n^y^ = mny^ — my^ = ny^ — y^, 
.*. mny^ — iny^ = ny^ — y^ ; 
mny^ — ^^^2 — ^J^a — Js • 
. ^r.n = ^'"^ + ""^y-y-^ ^ (m + n)y-y, , _ 

y. 7i ' * 

m-\-n^^-^-Ml^M', (99) 

y'-y.y-. 



_ y. —y^y. 
y" - yoy. 



(lOO) 



Equations (98) and (99) enable us to calculate numerically 
the values of M and JV from the five given values of log /. 
Then solving for m and n, 



M iM' ,,y 

M , iM'' ,,\* 



Solving one of the equations (97) for b^ 

b = 'Jlt^Ii = _«-^J'.^ . (,oi) 

n{in—\) — {m^—ni) {m — i){n — m) 



SATURATED VAPOR. 7 1 

Again, solving the first equation of (96) for c, 

_ ny, — y, 

•^° ;/ — in y, — my^ . 

c— = 7 — \t ^- • . (102) 

n — I \n — i){n — m) ^ / 

From the first equation of (95), 

a=\ogp,-b-c (103) 

I 
Finally, a = m*^-^o'^ (104) 

I 

/? =:;2^T^ (105) 

For temperatures below freezing-point Regnault used the 
equation 

p — a-\-ba^, (106) 

which is an equation to a curve passing through three points 
at equidistant temperatures, and of which the solution is very 
simple. 

Regnault's Data and Equations for Steam. — For equa- 
tion (106) the data are : 

t^ — — 32° C. /o = 0.32 mm. of mercury. 
t^= - 16° C. p, = 1.29 " 
/, ^ 0° C. A = 4-6o '' 



From which Regnault calculated the following equation, by aid 

of seven-place logarithms : 

A. For steam from — 32° to 0° C, 

p =z a -\- ba^ ; 

a—— 0.08038 ; 
log b — 9.6024724 — 10 ; 
log a = 0.033398 ; 

;2 rrr 32° - t. 



72 THERMODYNAMICS OF THE STEAM-ENGINE. 

Regnault gives three equations of the form given by equa- 
tion (97), of which the following are the data : 

B. t^ = 0° C. /o = 4-6o mm. of mercury. 



D. 



^.= 25° 


C. 


A = 


23-55 


u 


n 


^.= 50° 


c. 


A = 


91.98 


(( 


« 


^3= 75° 


c. 


A = 


288.50 


n 


u 


t,= 100° 


c. 


A = 


760 


u 


u 


t, = 100° 


c. 


A = 


760 


n 


« 


^.= 130° 


c. 


A = 


2030 


« 


« 


t, = 160° 


c. 


A = 


4651.6 


(( 


« 


t, = 190° 


c. 


A = 


9426 


« 


(( 


t, = 220° 


c. 


A = 


17390 


u 


( 


^o--20^ 


'C. 


A = 


0.91 


<< 


« 


^x = +40' 


°c 


A = 


54.91 


<( 


« 


t, = 100° 


c. 


A = 


760 


u 


(( 


^3 = 160° 


c. 


A = 


4651.6 


(( 


« 


/, r= 220° 


c. 


A = 


17390 


« ' 


« 



And from these data he calculated, by aid of seven-place 
logarithms, the following equations, which are correct at Paris : 

B. For steam from 0° to 100° C, 

log / = <^ — da^ -}- cfi» ; 

^ = 4.7384380; 
log d = 0.61 16485 ; 
log c = 8.1340339— 10; 
log a = 9.9967249 — 10; 
log J3 = 0.006865036 ; 



SATURATED VAPOR, 73 

C. For steam from ioo° to 220° C, 

log p ^^ a — boc^ 4" ^fi**^ » 

a = 54583895 ; 

log d = 0.41 2 1470; 
log c = 7.7448901 — 10; 
log a = 9.997412127 — 10; 
log /3 = 0.007590697 ; 
n = t — 100. 

D. For steam from — 20° to 220° C, 

log p = a — da» — ^/J« ; 

a = 6.2640348 ; 
log ^ = 0.1397743; 
log ^ = 0.6924351 ; 
log a = 9.994049292 ; 
log /3 = 9.998343862 ; 

;^ = / + 20. 

The temperatures and pressures of saturated steam in the 
tables given by Regnault were calculated by equations A and 
B for their respective ranges, but equation D was used instead 
of C for temperatures above 100° C. 

Wishing to attain greater accuracy for meteorological work, 
Moritz recalculated equation B, using ten-place logarithms 
and obtained constants that differed but little from those which 
will be given later. Some of the more recent tables in the 
French system were calculated by aid of his equation. 

Equations for the Pressure of Steam at Paris. — In 
view of the preceding statements it appeared desirable to re- 
calculate the constants for equations B and C with such a degree 
of accuracy as to exclude any doubt as to the reliability of the 
results. Accordingly the logarithms of the five values of / for 
each equation were taken from Vega's ten-place table, and then 
the remainder of the calculations were carried on with natural 
numbers, checking by independent methods, with the follow- 
ing results : 



f^ THERMODYNAMICS OF THE STEAM-ENGINE. 

B. For steam from o° to ioo° C, 

\og p — a — ba'' -\r c^"", 

a — 4.7393622142 ; 
log b — G.61 17400190 ; 
log c= 8.1320378383- 10; 
log or = 9.996725532820 — 10 ; 
log yS =z 0.006864675924 ; 

n ^=:^ t, 

C. For steam from 100° to 220 C, 

log p ^ a — ba"^ 4" ^/5« ; 

^ = 54574301234; 
log /^r= 0.41 1978793 1 ; 
log ^ = 7.7417476470- 10; 
log a = 9.997 A^ 106346 — 10 ; 
log /? = 0.0076424891 13 ; 

n — t— 100. 

To show the degree of accuracy attained, the following 
tables are given : 

EQUATION B. 



/. 


/. 


log/ from table of 
logarithms. 


log/ calculated by- 
equation. 





4.60 

23-55 
91.98 

288.50 

760 


0.6627578317 
1.3719909115 
1.9636934052 
2.4601458175 
2.8808135923 




25 
50 

75 
100 


I. 37199097 
1.96369346 
2.46014587 
2.88081365 



EQUATION C. 



t. 


p. 


log / from table of 
logarithms. 


log/ calculated by 
equation. 


100 


760 

2030 

4651.6 

9426 
17390 


2.8808135923 
3 3074960379 
3.6676023618 

3.9743274354 
4.2402995820 




130 
160 
190 

220 


3.307496036 
3.667602359 
3.974327428 
4.240299575 



SATURATED VAPOR. 75 

The results from equation C are quite satisfactory, for the 
errors come in the ninth place of decimals, and one place of 
decimals is unavoidably lost in the application of the formula. 
Equation B was calculated after equation C, and the numerical 
work was not carried to so large a number of decimal places. 
For the calculation of tables, the constants are carried to seven 
places of significant figures only ; this gives six places in the 
result, of which five are recorded in the table. 

Pressure of Steam at Latitude 45°, — French System. — 
It is customary to reduce all measurements to the latitude of 45°, 
and to sea level. The standard thermometer should then have 
its boiling and freezing points determined under, or reduced to, 
such conditions. The value of g, the acceleration due to 
gravity given by equation (58), is 9.809218 meters at Paris, 
latitude 48° 50^ 14'^ and at an elevation of 60 meters. At 45° 
and at sea level, g ■=. 9.806056 ; consequently 760 mm. of mer- 
cury at 45° latitude give a pressure equal to that of 

980.6056 
760 X ^g^;^ = 759-755 mm. 

at Paris, and by equation B this corresponds to a temperature 
of 99°.99i C. In other words, the thermometer which is stand- 
ard at 45° has each degree 0.99991 of the length of the degree 
of a thermometer standard at Paris. 

Again, we have that the height of a column of mercury at 

980.9218 
45° latitude is — ; — ;; — 7 times the heisfht of a column which will 
^ 980.6056 ^ 

give the same pressure at Paris. Consequently, to reduce equa- 
tion B to 45° latitude, we have 

1 . 11 q8o.q2i8 , ^ , ^ 

log p ^ a A- lop; - — - — - — ^af°-9959i^J_^/5 0.99991/. 

980.6056 ' ^ 

and for equation C, 

log^ = a A- logr ^ — !^ — _ — ^^(0.99991^-100) j_^yp (0.99991/ -100) 
980.6056 ' 

, , 980.9218 , , , 

= a -\- loP" z: aa~ °-°°9 a 0-99991 (^ - 100) 

' ^ 980.6056 

-}- C^~ °-°°9 ^ 0.99991 (/ - loo) ^ 



^6 THERMODYNAMICS OF THE STEAM-ENGINE, 

The resulting equations are: 

B. For steam from o° to ioo° C. at 45° latitude, 

log p = a,— ba,'' + cfS^"" ; 

^x = 47395022 ; 
log <5 = 0.61 1 7400190; 
log c = 8.1320378383 — 10; 
logoTj = 9.996725827522 — 10 ; 
log/?j = 0.006864058103 ; 

n = L 

C. For steam from 100° to 220° C. at 45° latitude, 

^1 = 5-457570I ; 
log ^, — 0.4120020935 ; 

log c^ = 7,7416788646 — 10 ; 
log or, =z 9.99741 1296464 — 10; 
log/?j= 0.007641 801 289; 
n = t — 100. 

Pressure of Steam at Latitude 45°,— English System. — 

To reduce the equations for the pressure of steam, so that 
they will give the pressures in pounds on the square inch for 
degrees Fahrenheit, there are required the comparison of 
measures of length and of weight, the comparison of the scales 
of the thermometers, and the specific gravity of mercury. 

Professor Rogers* gives for the length of the meter, 39.3702 
inches. This differs from the value given by Captain Clarke f 
by an amount that does not affect the values in the tables ; his 
value being 39.370432 inches. 

Professor Miller :j: gives for the weight of one kilogram, 
2.26462125 pounds. 

Regnault § gives for the weight of one liter of mercury, 
13.5959 kilograms. 

* Proceedings of the Am. Acad, of Arts and Sciences, 1882-83; also addi- 
tional observations. 

f Proceedings of the Royal Society, vol. xv. 1866. 
t Philosophical Transactions, cxlvi. 1856. 
^ Memoires de I'lnstitut de France, vol. xxi. 



SATURATED VAPOR. y/ 

The degree Fahrenheit is f of the degree Centigrade. 
135959 X 2.204621 



Let k — 



39-3702 



then equations B and C have for the reduction to degrees 
Fahrenheit, and pounds on the square inch, 

log/ = ^, + log /^ — ba^i'' -\- cjS}'' ; 

log p = a,-^\ogk- tyf + c.p^'' . 

The resulting equations are : 

B. For steam from 32° to 212° F. in pounds on the square 
inch, 

log/ ^a,-ba--Ycp-\ 

a^ — 3.025908 ; 
log b = 0.61 17400 ; 
log c — 8.13204 — 10 ; 
log ^'2 = 9.998181015 — 10; 
log A =0.0038134; 
n — t — '^2. 

C. For steam from 212° to 428° F. in pounds on the square 
inch, 

log / = ^, - b,a^^ -f- ^^^/ ; 

^. = 3743976 ; 

log b^ — 0.4 1 2002 1 ; 
log c, = 7.74168 — 10 ; 
log a^ = 9.998561831 — 10; 
log A = 0.0042454 ; 
n= t — 212. 

Other Equations for the Pressure of Steam.— Rankine* 
gives the following equation for the pressure of saturated steam, 

\ogp = A-^-Y', (107) 



* Steam-engine and Other Prime Movers. 



78 



THERMODYNAMICS OF THE STEAM-ENGINE. 



in which T is the absolute temperature calculated by the 
equation 

For pounds on the square foot the values of the constants are 

A = 8.2591 ; log .5 := 3.43642 ; logC= 5-59873- 
For pounds on the square inch the only change is 

A = 6.1007. 

This equation has the advantage that it may be solved 
directly for T, a property that Regnault's equations do not 
have. It gives quite accurate results, and the greater part of 
English tables of properties of saturated steam are calculated 
by its aid. The following table will give a comparison between 
the results from this formula and those from formulae B and C. 

RANKINE'S EQUATION FOR STEAM. 



Temperature 
(Fahrenheit). 


Pressure, pounds per square inch. 


Regnault at 45° 
latitude. 


Rankine. 


32° 

. 77 

122 

167 

212 

257 
302 

347 
392 
428 


0.0890 

0.4555 
1.7789 

5-579 
14.697 

33-711 

69.27 
129.79 
225.56 
336.26 


0.083 
0.452 
1.78 
5.58 
14.70 

33-71 
69.21 

129.8 

225.9 

336.3 



A number of exponential formulae have been devised, of 
which the principal advantage is the facility of application. 
The following, by Magnus, gives pressures in mm. of mercury 
for degrees Centigrade, and agrees quite well with Regnault's 
results below ioo°, but is not so correct above ioo° : 



7-4475 f 

p — 4.525 X 10^34.69 + ^ 



(108) 



SATURATED VAPOR. 79 

The table following exhibits the defects of equation (108) : 

MAGNUS' EQUATION FOR STEAM. 



Temperature 
(Centigrade). 


Pressures, mm. cf mercury. 


Regnault at 45° 
latitude. 


Magnus. 


0° 

50 

100 

150 

200 


4.602 
91.98 
760.0 
3581.9 
I 1664. 


4-525 
91.97 
759-9 
3627. 
12080. 



Pressure of Other Vapors. — Regnault * determined also 
the pressure of a large number of saturated vapors, at various 
temperatures, and deduced equations for each in the form of 
equation (94). The equations and the constants as determined 
by him for the commoner vapors are given in the following table : 



PRESSURE OF SATURATED VAPORS. 





log/ 


a 


b 


c 


Alcohol 


a — ban^ cfin 
a + ba^- c/3^ 
a — ba-^ — c/3» 
a — ba^ — c/3^ 
a-ba^ — c(3^ 


5.4562028 
5.0286298 

5-2253893 

5.40I1662 

12.0962331 


4.9809960 
0.0002284 
2.9531281 
3.4405663 
9.1375180 


0.0485397 
3.1906390 
0.0668673 
0.2857386 
1.9674890 


Ether 


Chloroform 


Carbon bisulphide 

Carbon tetrachloride.. 



Alcohol 

Ether 

Chloroform 

Carbon bisulphide. . . . 
Carbon tetrachloride.. 



log a 



1.99708557 
0.0145775 
I. 9974144 
1.9977628 
I. 9997 I 20 



log^ 


n 


1.9409485 


t-\- 20 


1.996877 


/+ 20 


I. 9868176 


/ — 20 


T.99II997 


/-j- 20 


1.9949780 


t-\- 20 



Limits. 



- 20°, + 150° C. 

- 20°, + 120° C. 
+ 20°, -f 164° C. 

- 20°, + 140° C. 
-20°, + 188° C. 



*Academie des Sciences, Comptes rendus, Tome xxxvi. 



80 THERMODYNAMICS OF THE STEAM-ENGINE. 

Zeuner* states that there is a slight error in Regnault's cal- 
culation of the constants for aceton, and gives instead, 

log / —a — ba"" + c/5« ; 

^== 5-3085419; 
log ^^'^ = + 0.5312766 — 0.0026 1 48/f; 
log c^"" = — 0.9645222 — 0.0215592/. 



Differential Coefficient ^. — From the general form of the 
equation (94), we have 



log./ = ^^ + ;^^^^ + ^^y5%. . . . (109) 



M being the modulus of the common system of logarithms. 
Differentiating, 



■^- = -^l>log,a.a^ + -L,log,^.^n. 



or, reducing to common logarithms, 



If^^Aa' + BP" (.,0) 



For saturated steam at 45° latitude, the constants to be 
used with equation (i 10) are : 

* Mechanische Warmetheorie. 



SATURATED VAPOR, 8 1 

French units, 

B. For o° to 100 C, mm. of mercury, 

\o%A = 8.8512729— 10; 
log B — 6.69305 — 10; 
log «', = 9.996725828 — 10; 
log/?i = 0.0068641. 

C. For 100° to 220° C, mm. of mercury, 

log^ = 8.5495158-10; 
log ^ = 6.34931 - 10; 
log ^, = 9.997411296— 10; 
logy^i = 0.0076418. 

English units. 

B, For 32° to 212° F., pounds on the square inch, 

log A — 8.5960005 — 10; 
log B = 6.43778 - 10 ; 
logos', = 9.998181015 — 10; 
log A = 0.0038134. 

C. For 212° to 428° F., pounds on the square inch, 

log ^ =8.2942434- 10; 
log B = 6.09403 — 10; 
logo', = 9.998561831 — 10; 
log/Jj = 0.0042454. 

dp 
It is to be remarked that -3- may be found approximately 

by dividing a small difference of pressure by the corresponding 



82 



THERMODYNAMICS OF THE STEAM-ENGINE. 



difference of temperature ; that is, by calculating 



Ap 
'At' 



With a 



table for even degrees of temperature, we may calculate the 
value approximately for a given temperature by dividing the 
difference of the pressures corresponding to the next higher and 
the next lower degrees by two. 

The foflowing table of constants for the several vapors 
named were calculated by Zeuner from the preceding equa- 
tions for temperature and pressure of the same vapors : 



DIFFERENTIAL COEFFICIENT. 



/ dt' 



Alcohol 

Ether 

Chloroform 

Carbon bisulphide. . 
Carbon tetrachloride 
Aceton 



Sign. 



Ao.^ Bp 



+ 



log(^a«) 



1720041 — 0.0029143/ 
3396624 — 0.0031223^' 
3410T30 — 0.00258562! 
4339778 — 0.0022372/ 
8611078 — 0.0002880/ 
3268535 — 0.0026148/ 



log (^/3«) 



- 2.9992701 — 


05905^52? 


— 4-4616396 + 


o'4S775'' 


— 2.0667124 — 


0131824/ 


— 2.05II078 — 


0088003/ 


— I.38I2I95 — 


00":0220/ 


— 1.9064582 — 


0215592/ 



Heat of the Liquid and Specific Heat. — A preliminary 
series of experiments convinced Regnault that the specific heat 
of water at low temperature is unity. To test the specific heat 
at higher temperatures he ran hot water from a boiler, and at 
a known temperature, into a calorimeter in which the temper- 
ature varied from 8° to 14° C, and the resulting upper temper- 
ature varied from 17° to 29° C. Knowing the original weight 
of water in the calorimeter,, the weight run in from the boiler, 
and the initial and final temperatures in the calorimeter, he 
calculated the mean specific heat of water between the tem- 
perature of the boiler and the final temperatures of the calo- 
rimeter. A series of forty such experiments was made, with 
the temperature of the boiler varying from 108° to 192° C, 
from which Regnault concluded that the mean specific heat 
from 0° to 100° is 1.005, ^^^ from 0° to 200°, 1.016. The cor- 



SATURATED VAPOR. 83 

responding heat of the liquid, i.e., the heat required to raise one 
kilogram of water from 0° to a given temperature, t, is : 

For 100°, .... 100.5 ; 
" 200°, .... 203.2. 

Assuming an equation of the form 

q = t-\-Af-\-Bt\ (ill) 

and solving for the two constants by aid of the two known values 
of q, the following equation, which is commonly used, is deduced : 

^ z= ^ -f 0.00002^' -f 0.0000003/'. • • • (112) 

The specific heat at any temperature is, therefore, 



c = ~ — I + 0.00004/ -|- o.oooooo9/^ . (113) 



These equations are for use with the Centigrade scale ; for 
the Fahrenheit scale, a given temperature may be reduced to 
the Centigrade scale, and then introduced in the same equations. 

The process of making the experiments is really a complex 
one ; for the water in leaving the boiler has work done on it by 
the steam pressure in the boiler, and it has a certain velocity 
impressed on it at the same time, and again, in entering the 
calorimeter, it does work against the atmospheric pressure, and 
the kinetic energy of its motion is changed into heat. At 
higher temperatures there is a double change of state ; part of 
the water changes to steam on leaving the boiler, and that 
steam is condensed again in the calorimeter. It is probable 
that the error of neglecting the effect of these several actions 
is inconsiderable. 



84 THERMODYNAMICS OF THE STEAM-ENGINE. 

The degree of accuracy to be accorded to this work is in- 
dicated by the fact that Regnault gives four significant figures 
in stating the data for the calculation of the constants in the 
equations. 

Sirhilar experiments were made to determine the heat of 
the liquid of other volatile liquids, the results of which were as 
follows : 

HEAT OF THE LIQUID. 
Alcohol q = o. 54754/ + 0-OOII2l8i'2 

-\-O.QQ>Q)0022Q)tt^. 

Ether ^ = 0.52901/-!- 0-0002959/^ 

Chloroform q = o. 23235/ -[- 0.0000507/^ 

Carbon bisulphide q — 0.23523/4- 0.000081 5/^ 

Carbon tetrachloride q = 0.19798/-}- 0.0000906/^. 

Aceton q = 0.50643/4-0.0003965/^. 

The specific heat at any temperature may be obtained by dif- 
ferentiating the equations for the heat of the liquid, thereby 
obtaining equations like equation (113). 

Rowland's Experiments. — A series of experiments was 
made by Rowland '^ at Baltimore to determine the mechanical 
equivalent of heat, which gave a delicate method of determin- 
ing the heat of the liquid and the specific heat. 

The apparatus used was similar to that used by Joule, with 
modifications to give greater certainty of results. The calo- 
rimeter was of larger size, and the paddle had the upper vanes 
curved like the blades of a centrifugal pump, to give a strong 
circulation up through the centre, past the thermometer for 
taking the temperatures, and down at the outside. The paddle 
was driven by a petroleum engine, and the power applied was 
measured by making the calorimeter into a friction brake, with 
two arms at which the turning moment was measured. Radia- 
tion was made as small as possible, and then was made deter- 
minate by use of a water-jacket outside of the calorimeter. 

The experiments consisted essentially in delivering a meas- 

* Proceedings of the American Academy, vol. xv. (N. S. vii.). 1879. 



SATURATED VAPOR. 



85 



ured amount of work to- the water in the calorimeter, and in 
noting the rise of temperature produced thereby. 

The whole range covered by the experiments was from 2° 
to 41° C. The results show that 430 kilogrammeters of work 
are required to raise one kilogram of water from 2° to 3° C. 
Assuming that the same amount will be required to raise the 
same weight from 0° to 1°, and from 1° to 2°, the following 
table has been arranged from Rowland's final table of results : 

ROWLAND'S MECHANICAL EQUIVALENT OF HEAT. 




In the above table, column i gives the number of degrees 
above freezing on the Centigrade scale ; column 2 gives the 
number of kilogrammeters required to raise one kilogram of 
water from freezing-point to the given temperature ; column 3 
is Rowland's mechanical equivalent of heat at the given tem- 
perature derived from 10° intervals on column 2 ; column 4 is 
obtained by dividing the numbers in column 2 by the mechani- 



86 THERMODYNAMICS OF THE STEAM-ENGINE. 

cal equivalent of heat at i6f ° C, or 62° F., from column 3 ; and 
column 5 is calculated by considering the specific heat to be 
constant for each five degrees of temperature. These specific 
heats were derived from a curve obtained by plotting tempera- 
tures for abscissae, and heats of the liquid for ordinates. The 
values of the specific heats will be given later in connection 
with those for higher temperatures. 

A review of the preceding table shows that the specific heat 
at low temperatures varies quite markedly, so that it appeared 
advisable to investigate the effect of this variation on Regnault's 
experiments already quoted. This was done quite expeditiously 
by multiplying the mean specific heat given by him for his. 
several experiments by the true average specific heat for the 
range of temperature in the calorimeter. This corrected specific 
heat was then used to calculate the increase of heat from the 
final temperature of the calorimeter to the temperature of the 
boiler, and that increase was added to the heat of the liquid 
from the table to find the heat of the liquid at the temperature 
of the boiler. The results were then plotted as before, and 
compared with the heats of the liquid derived from Regnault's 
mean specific heats uncorrected. The points by the corrected 
method were a little more regularly arranged than the points 
obtained by assuming the specific heat to be unity, at low tem- 
peratures ; but the improvement was inconsiderable. The in- 
equality of the specific heat at low temperatures is seldom sa 
much as the unavoidable errors of the method. 

It appeared that if the specific heat was assumed to be con- 
stant, from 40° to 45°, from 45° to 155°, and from 155° to 
200° C, the straight lines thus drawn represented the experi- 
mental values as recalculated quite nearly ; and further, they 
represented the uncorrected experimental values more nearly 
than Regnault's equation. 

Specific Heat of Water. — The combination of Rowland's 
and Regnault's experiments on the heat of the liquid by the 
method described gives the specific heats set down in the fol- 
lowing table : 



SATURATED VAPOR. 
SPECIFIC HEAT OF WATER. 



87 



Range. 


Specific Heat. 


Centigrade. 


Fahrenheit. 


O to 5 
5 to lO 
10 to 15 
15 to 20 
20 to 25 
25 to 30 
30 to 35 
35 to 40 
40 to 45 
45 to 155 
155 to 200 


32 to 41 

41 to 50 

50 to 59 

59 to 68 

68 to 77 

77 to 86 

86 to 95 

95 to 104 

104 to 113 

113 to 311 

311 to 392 


1.0072 

1.0044 

1.0016 

I. 

0.9984 

0.9948 

0.9954 

0.9982 

I. 

1.008 

1.046 



Standard Temperature. — In the beginning of our work it 

was stated that we siiould use 62° F. for our standard tempera- 
ture ; and the reasons for so doing may now be shown. We 
know actually nothing about the specific heat of water from 
0° to 2° C. ; consequently, the commonly accepted value of the 
thermal unit, ?>., the heat required to raise one unit of weight 
of water from 0° to 1° C, or from 32° to 33° F., is an ideal 
quantity inferred from the behavior of water at higher tem- 
peratures. It is more scientific to take an easily verified 
quantity for the standard ; and there is a practical convenience 
in choosing 62° F. for the standard temperature, because it is 
near the mean temperature of the air during experimental 
work. Therefore, it is near the mean temperature in the calo- 
rimeter during ordinary work with that instrument ; and the 
specific heat of water for the range of temperature in the calo- 
rimeter may usually be considered to be unity, without error, 
unless great refinement is desired. 

Mechanical Equivalent of Heat. — The mechanical equiv- 
alent in meter-kilograms of one calorie at i6|-° C, deduced from 
Rowland's experiments in the third column of the table on 
page 85, is 427.1. 

Since the value given by Joule is commonly quoted, it will 
be of interest to make a comparison of his latest work (1873) 
with Rowland's, as given in the following table: 



88' THERMODYNAMICS OF THE STEAM-ENGINE. 

COMPARISON OF ROWLAND'S AND JOULE'S EXPERLMENTS. 



Temperature. 


Joule's Value at 

Manchester, 
English System. 


Reduced to the Air Thermometer 
and to the latitude of Baltimore. 


Rowland's Value, 
Corresponding. 




English. 


French. 


12°. 7 

15°. 5 
1.4°. 5 
17°. 3 


772-7 
774-6 
773-1 
767.0 
774-0 


776-1 
778.5 
776.4 
770.5 
777.0 


425-8 
427.1 
426.0 
422.7 
426.3 


427-6 
428.0 
427.3 
427.5 
426.9 



The value of g at Baltimore, latitude 39° 17^ is 980.05 
centimeters ; therefore, reducing to 45° of latitude and at the 
sea level, the value of J is 



427.1 Xf ^ = 426.86, 
980.6056 



or, as it has been given before, 

/ — 426.9. 

To reduce to the English system, multiply by |^, and by the 
length of the meter in feet, so that 

/=778. 



Total Heat. — This term is defined as the heat required to 
raise a unit of weight of water from freezing-point to a given 
temperature, and to entirely evaporate it at that temperature. 
The experiments made by Regnault were in the reverse order ; 
that is, steam was led from a boiler into the calorimeter and 
there condensed. Knowing the initial and find weights of the 
calorimeter, the temperature of the steam, and the initial and 
final temperatures of the water in the calorimeter, he was able, 
after applying the necessary corrections, to calculate the total 
heats for the several experiments. 



63°, 



SATURATED VAPOR. 89 

As a conclusion of the work he gives the following values 
for the total heats 

. . 610 By equation, 609.6 
. . 625 625.2 

. . 637 
195°, ... 666 

Assuming an equation of the form 

\=. A^ Bt, (114) 

Regnault calculated the constants from the values given for 
100° and 195°, and gives the equation 

A = 606.5 + 0.305^' (115) 

In order to see the effect of the varying value of the specific 
heat at low temperatures, the total heats given by experiment 
were recalculated by a method resembling that used in recalcu- 
lation of the heats of the liquid, and the results plotted to- 
gether with Regnault's values uncorrected. The recalculated 
points were a little more regular than the original ones, and lay 
nearer the line represented by the equation (115). Especially 
did the recalculated points for those experiments, for which the 
true mean specific heat of the water in the calorimeter was 
nearly unity, lie near that line. It therefore appears that 
equation (115) represents our best knowledge of the total heat 
of steam. 

For the Fahrenheit scale the equation becomes 

A == i09i.7 + o.305(^'- 32) (116) 

Regnault gives the equations following for other liquids : 

Ether A. = 94 -[-0.45^ —0.00055556^2 

Chloroform A= 67 -|- 0.1375/. 

Carbon bisulphide A= go -|-o. 14601^' — 0.0004123/^ 

Carbon tetrachloride A = 52 -f- o. 14625/ — 0.000172?'' 

Aceton X = 140. 5 + o- 36644/ — 0.0005 16/''' 

Heat of Vaporization. — If the heat of the liquid be sub- 
tracted from the total heat, the remainder is called the heat 
of vaporization, and is represented by r, so that 

r^\-q (11;) 



90 



THERMODYNAMICS OF THE STEAM-ENGINE. 



Specific Volume of Liquids. — The coefficient of expan- 
sion of most liquids is large as compared with that of solids, 
but it is small as compared with that of gases or vapors. 
Again, the specific volume of a vapor is large compared with 
that of the liquid from which it is formed. Consequently the 
error of neglecting the increase of volume of a liquid with the 
rise of temperature is small in equations relating to the ther- 
modynamics of a saturated vapor, or of a mixture of a liquid 
and its vapor when a considerable part by weight of the mix- 
ture is vapor. It is therefore customary to consider the spe- 
cific volume of a liquid a to be constant. 

Experiments were made by Hirn * to determine the volumes 
of liquid at high temperatures compared with the volume at 
freezing-point, by a method which was essentially to use them 
for the expansive substance of a thermometer. The results 
are given in the following equations : 



SPECIFIC VOLUMES OF HOT LIQUIDS. 







Logarithms 




Water, 

100° C. to 200° C. 

(Vol. at 4° = unity.) 


V = \-\- 0.00010867875^ 

-|- 0.0000030073653/2 

-|- 0.000000028730422/^ 

— 0.0000000000066457031/4 


6.0361445 - 

4.4781862 — 
I. 4583419 - 
8.8225409 — 


10 
10 
10 
20 


Alcohol, 

30° C. to 160° C. 

(Vol. at 0° = unity.) 


V = \ At 0.00073892265/ 
4- 0.00001055235^2 

— 0.000000092480842^^ 
-{- 0.00000000040413567/4 


6.8685991 — 
3.0233492- 
2.9660517 — 
0.6065278 — 


10 
10 
10 
10 


Ether, 

30° C. to 130° C. 

(Vol. at 0° =r unity.) 


z/ = I + 0.0013489059/ 
-j- 0.0000065537/2 
— 0.000000034490756/3 
+ 0.00000000033772062/4 


7.1299817- 
4.8164866 — 
2.5377028 - 
0.5285571- 


10 
10 
10 
10 


Carbon Bisulphide, 

30° C. to 160' C. 
(Vol. at 0" = unity.) 


V —\-\- 0.0011680559/ 

-j- 0.0000016489598^2 

— 0.0000000008 1 1 19062/3 
-|- 0.000000000060946589/4 


7.0674636- 
4.2172103 - 
0.9091229 — 
9.7849494- 


10 

10 
10 
20 


Carbon Tetrachloride, 

30° C. to 160° C. 

(Vol. at 0° = unity.) 


V ■=. 1 -\- 0.0010671883/ 

-j- 0.0000035651378/2 
— 0.00000001494928 1/3 
-f- 0.000000000085 1 82318/4 


7.0282409 — 
4.5520763- 
2.1746202 - 
9.9303494- 


10 

10 

- 10 

20 



*Annales de Chimie et de Physique, 1867. 



SATURATED VAPOR. 9 1 

Internal and External Latent Heat. — The heat of vap- 
orization overcomes external pressure, and changes the state 
from liquid to vapor at constant temperature and pressure. Let 
the specific volume of the saturated vapor be j, and that of the 
liquid be (X, then the change of volume is ^ — cr = ^^, on pass- 
ing from the liquid to the vaporous state. The external work is 

p(s-&)=pu, ...... (118) 

and the corresponding amount of heat, or the external latent 
heat, is 

Ap{s—(f) — Apu (119) 

The heat required to do the disgregation work, or the in- 
ternal latent heat, is 

p = r — Apu, (120) 

Specific Heats of Water and Steam. — In the general 
discussion of thermodynamics and the application to gases two 
kinds of specific heat were used, at constant volume and at 
constant pressure. In dealing with solids and with liquids be- 
low the boiling-point the only specific heat that has been 
determined is the specific heat at constant pressure : for exam- 
ple, the specific heat of water determined from Rowland's ex- 
periments is of that sort. For most solids and liquids the 
specific heat at constant volume cannot be very different from 
the specific heat at constant pressure, and it is commonly 
assumed that they are identical. 

If a given substance experience a change of temperature 
under a specific condition, then the heat required to change the 
temperature of a unit of weight one degree is the specific heat 
under that condition. There will, therefore, be as many kinds 
of specific heat as there are conditions. In dealing with a mix- 
ture of a liquid and its vapor, for which the pressure is a func- 
tion of the temperature only, the specific heat for each is defined 
under the condition that the pressure shall vary with the tem- 
perature, according to the law of saturated vapor given by the 
general equation (94). 



92 THERMODYNAMICS OF THE STEAM-ENGINE. 

Let c be the specific heat of water under the given condi- 
tions. The meaning may be deduced from equation (6) appHed 
to pure liquid, 

dp\ 



dQ = [cp4-m^^dt\ 



dQ dp 



For water we may use ^, the heat of the liquid, for Q, and 
then 

dq dp 



The only reason for writing the last equation is to give a 
clearer conception of the subject, for no experimental work exists 
for its use. Regnault's experiments probably give c rather than 
Cp . In any case no attempt is made in thermodynamics to dis- 
tinguish between the different kinds of specific heat for water. 

The specific heat of saturated steam, i.e.^ the heat that must 
be given to one unit of weight of steam, when the temperature 
is raised one degree and the pressure raised the corresponding 
amount, in order that the steam shall remain dry and satu- 
rated, is represented by h. An equation having the form of 
equation (121) cannot be employed, since the temperature can- 
not be raised without raising the pressure at the same time. 
An investigation of other properties of steam will determine 
the form and value of this function. 

General Equation. — A pound or a kilogram of a mixture 
of a liquid and its vapor consists of a certain part, x^ of vapor, 
and the remainder, i —x, of liquid. The specific volume of 
the mixture is 

z; = ;ir^ -|- (i — x)a- = (5 — (t)x -\- a — zix -^ cr. . (122) 



SATURATED VAPOR, 93 

When a mixture of liquid and a vapor receives heat, there 
is in general an increase of temperature of each component, 
and a change of part of the liquid into vapor. 



. • . dQ — hxdt + c{\ — x)dt + rdx. . . (123) 

Application of the First Law. — Proceeding as we have 
in our preceding work, equations (24) and (127) give 

dQ — A{dE -{-pdv) = hxdt + c{\ — x)dt -\- rdx ; 
hx-\- c{\ — x^ \dt-\-~^dx— pdv. 



dE = ^ 



(di 

dt 






d'E d'E 
Smce 



dx dt dt dx ' 



d j I 
di\^ 



^+'c-')]-K3,l,=£5-HS),] 



Bearing in mind that h, c, and / are functions of t and not 
of X, the differentiation gives 

I d'v _ I ldr\ idp\ ldv\ d'^v 

A^ ^^~^d^dt ~ A\dtK ~ [dtlSdxJ, ~^didx' 



94 THERMODYNAMICS OF THE STEAM-ENGINE, 

But 

d'^v _ d'v {dp\ _dp^ (d7\ _ dr 

l^t ~ Itdx \dtK ~ dt Vdt)^ ~ ~dt ' 

From equation (122), o- being constant, 
' dv\ 



(i). = ^= 



,.,^^c-h=Au^ (124) 

dQ 
Application of the Second Law. — By this law -^ is a 

perfect differential. 



dQ kx A- c{i — x) , , r ^ 
.-. -Y= ~ X -dt-\-^dx, . . (125) 



dx dt dt dx ' 

d Vhx -^ c{\ — xy\ d(r\ , ^, 



But 



^dr 

h — c dt 



* * dt 



dr , , r f K 

+ c - h = -^ (127) 



SATURATED VAPOR. 95 

First and Second Laws Combined. — The combination 
of equations (124) and (127) gives 



r=AuT-£. (128) 



Specific Heat of Steam. — Equation (127) solved for h gives 



''^'+it-T ('^9) 



Now r — \ — q = 606.5 -f- 0.305/ — q, 

and q calculated by the aid of the table on page 87 will have 
for its value 

q = const. -\- c(t — const.) ; 

hence we shall have 

dr 

-=0.305-.; 



^ = 0.305--^ (130) 



The term -^ may be calculated by aid of equation (115) and 

lie table on page 87, and then the following values of h may 
be calculated by equation (130) : 

SPECIFIC HEAT OF STEAM. 

o" C. 50° C. 100° C. 150° C. 200° C. 

h— — 1.911, — 1.461, — 1. 131, —0.879, —0.676. 



96 THERMODYNAMICS OF THE STEAM-ENGINE. 

The negative sign shows that heat must be abstracted from 
saturated steam when the temperature and pressure are increased, 
otherwise it will become superheated. On the other hand, 
steam, when it suddenly expands with a loss of temperature 
and pressure, suffers condensation, and the heat thus liberated 
supplies that required by the uncondensed portion. 

Hirn* verified this conclusion by suddenly expanding steam 
in a cylinder with glass sides, whereupon the clear saturated 
steam suffered partial condensation as indicated by the forma- 
tion of a cloud of mist. The reverse of this experiment showed 
that steam does not condense with sudden compression, as 
shown by Cazin. 

Ether has a positive value for h. As the theory indicates, 
a cloud is formed during sudden compression, but not during 
sudden expansion. 

The table of values of h for steam shows a notable decrease 
for higher temperatures, which indicates a point of inversion 
at which h is zero and above which h is positive, but the tem- 
perature of that point cannot be determined by our own ex- 
perimental knowledge. For chloroform the point of inversion 
was calculated by Cazinf to be I23°.48, and determined experi- 
mentally by him to be between 125° and 129°. The discre- 
pancy is mostly due to the imperfection of the apparatus used, 
which substituted finite changes of considerable magnitude for 
the indefinitely small changes required by the theory. 

Specific Volume and Density. — Solving equation (128) 
for u, we have 



dt 



which gives a method of calculating the increase of volume 



* Bulletin de la Societe Industr. de Mulhouse, cxxxiii. 
f Comptes rendus de I'Academie des Sciences, Ixii. 



SATURATED VAPOR. 9/ 

due to vaporization from experimental data» The specific 
volume s and density y are thus known from the equations 

S-U-\-(T, (132) 

y-1 (^33) 

It is of interest to consider the degree of accuracy that may 

be expected from this method of calculating the density of 

saturated vapor. The value of r depends on \ and q ; for the 

first Regnault gives three figures in the data from which the 

empirical equation is deduced, and the experimental work does 

not indicate a greater degree of accuracy. The fourth figure, 

if stated, is likely to be in error to the extent of five units. 

The value of T is commonly stated in four figures, of which 

the last may be in error by two units, A^ as determined by 

Rowland, has four figures, the last being uncertain to the ex- 

dp 
tent of one or two units. The differential coefficient — ,- is 

at 

deduced from the equations for calculating/; and those equa- 
tions are derived from data having five places of significant 
figures. Now each of the equations B and C, for steam at 45° 
latitude for the English system, gives a pressure of 14.6967 
pounds on the square inch ; but the specific volume calculated 
by aid of equation B is 26.550 cubic feet, while equation C 
gives 26.637 cubic feet. The mean, 26.60, differs from either 
extreme by about one in seven hundred. This discrepancy is 
due to the fact that the curves represented by equations B and 
C meet at the common temperature, 212°, but do not have a 
common tangent. Since the equations are empirical and not 
logical, the error or uncertainty is unavoidable, and all cal- 
culated specific? volumes are affected by a similar uncertainty* 
The greatest probable error is in determining r, for which it 
may be about one in one thousand. The error introduced into 
this equation by using the values of A in common use, that is, 
772 instead of 778, is about one in one hundred. 

The specific volume and density are commonly calculated 




98 THERMODYNAMICS OF THE STEAM-ENGINE. 

in the method given, on account of the great difficulty of the 
experimental determination, and the error of the method is 
not greater than that of the other parts of steam tables. 

Tate and Fairbairn's Experimental Determination. — 
The great uncertainty of the direct determination of the 
density of saturated vapor is due to difficulty 
of determining when steam is dry and satu- 
rated. A small quantity of liquid present, or a 
slight degree of superheating, will introduce 
serious errors. Fig. 26 is an ideal representa- 
tion of the saturation gauge used by Tate and 
Fig. 26. Fairbairn* in their experiments to determine 

this point. A and B are globes in which there is steam with a 
small quantity of water, having a communication by means of 
a tube partially filled with mercury. The globes and tubes are 
immersed in a bath by which all may be raised to any given 
temperature. So long as any water exists in both globes the 
pressure in both will be the same, and the mercury will be at 
the same level in both legs of the tube. As the tempera- 
ture rises the water in the globes will be gradually vaporized, 
till all in A^ containing the least amount, is changed into steam. 
At this instant the steam in A is dry and saturated, and if the 
weight and volume are known the density can be found. As 
the process goes on the steam in A becomes superheated, and, 
the pressure being less than for saturated steam at the same 
temperature, the mercury at a will rise. 

In making the experiments it was found advisable to super- 
heat the steam in A and then to let the temperature gradually 
fall, and to take a series of readings of the difference in height 
of a and b simultaneously with the readings of the thermom- 
eter in the bath, from which the temperature could be inferred 
at which the steam became saturated. At the same time the 
steam pressure was taken by a mercury column. The actual 
apparatus had a different appearance, and was arranged for 
convenience in observation, and had two forms, one for pres- 
sures above that of the atmosphere, and one for pressures below. 

* Philosophical Transactions, vol. cl. i860. 



SATURATED VAPOR. 



99 



The following table gives a summary of all of the experi- 
ments made. The second and third columns give the pressure 
and temperature of saturation; the fourth gives the relative 
volume compared with water ; the fifth gives the same volume 
by an empirical formula ; and the sixth gives the proportional 
error of the formula compared with the experimental value. 



TATE AND FAIRBAIRN'S EXPERIMENTAL DETERMINATION OF 
THE DENSITY OF SATURATED STEAM. 





Pressure in 
Inches of 
Mercury. 


Maximum 
Temperature 
of Saturation. 


Specific 
Volume from 
Experiment. 


Specific 

Volume from 

Formula. 


Error of 
Formula. 




P 


t 


V 


V 




I 


5-35 


136.77 


8275-3 


8183 


-^v 


2 


8.62 


155-33 


5333-5 


5326 


-yk 


3 


9-45 


159-36 


4920.2 


4900 


-^. 


4 


12.47 


170.92 


3722.6 


3766 


+ ^V 


5 


12.61 


171.48 


3715-1 


3740 


+ ri^ 


6 


13-62 


174.92 


3438.1 


3478 


+ 8V 


7 


16.01 


182.30 


3051.0 


2985 


-tV 


8 


18.36 


188.30 


2623.4 


2620 


+ ^k 


9 


22.88 


198.78 


2149.5 


2124 


-h 


i' 


53-61 


242.90 


943-1 


937 


-riy 


2' 


55-52 


244-82 


908.0 


906 


-^ 


3' 


55-89 


245.22 


892.5 


900 


+ TiT 


4' 


66.84 


255-50 


759-4 


758 


-Tk 


5' 


76.20 


263.14 


649.2 


669 


+ bV 


6' 


81-53 


267.21 


635-3 


628 


-eV 


i 


84.20 


269.20 


605-7 


608 


+ ^k 


8' 


92.23 


274.76 


584-4 


562 


-^v 


9' 


90.08 


273.30 


543-2 


545 


+ ^T 


lo' 


99.60 


279.42 


515-0 


519 


+ Tk 


ii' 


104 54 


2S2.58 


497-2 


496 


-Tk 


12' 


112.78 


287.25 


458.3 


461 


+ iiir 


13' 


122.25 


292-53 


433-1 


428 


-A 


14' 


114-25 


288.25 


449.6 


456 


-hyV 



The formula deduced by the experimenters to represent 
their work is 



F^::: 25.62 + 



49513 

P + o.;2' 



(134) 



lOO 



THERMODYNAMICS OF THE STEAM-ENGINE. 



in which V is the volume of steam compared with the volume 
of the water from which it was produced, and P is the pressure 
in inches of mercury. 

Although the experiments were made with great care and 
all precautions were taken to avoid error, the results are less 
satisfactory than those obtained by calculation from the other 
known properties of steam. 

To show the comparison between the values of the specific 
volume determined by the two methods, the following table 
has been calculated for English units : 

SPECIFIC VOLUME OF SATURATED STEAM. 



Pressure, 


Specific Volume, Cubic Feet per Pound. 


Pounds per Square 
Inch. 


r dt . 


-=--+pm- 


5 
15 

25 
35 

45 

55 


73.2 
26.2 
16. 1 

II. 7 
9-3 

7-7 


73-2 
25.8 
15.8 
II. 4 
9.0 
7-5 



Zeuner's Equation for Internal Latent Heat. — To 

avoid the laborious calculation of this quantity by the exact 
methods, Zeuner has proposed the following simple empirical 
equations for that purpose in the French system : 

INTERNAL LATENT HEAT. 

Water /o = 575.40 — 0.791^ 

Ether p — 86.54 — 0.10648^ — 0.0007160^^^ 

Chloroform p— 62.44 — o. 11282/ — 0.0000140/2 

Carbon bisulphide p= 82.79 — 0.11446/ — 0.0004020/''' 

Carbon tetrachloride p — 48.57 — 0.06844/ — 00002080/^ 

Aceton p = 131.63 — 0.20184/ — 0.0006280/^ 

The following table shows that the equation for water 
gives a fair degree of approximation : 

0° 50° 100° 150° 200° 

By equation (120) 575.5 536.3 496.4 457.4 417.4 

By empirical equation 5754 535-9 496.3 456.8 417.1 



SATURATED VAPOR. lOI 

Critical Temperature. — The empirical equation, and also 
the value of p in the table above by the exact method, show 
that the internal latent heat decreases as the temperature rises, 
and at sufficiently high temperatures it will approach zero. If 
p is made zero in Zeuner's equation for water, the corre- 
sponding temperature is 720° C, which indicates that the true 
point is much beyond the limits of experiments. 

The temperature at which p becomes zero for any vapor is 
called the critical temperature, for at that temperature the dis- 
tinction between the liquid and its vapor vanishes, and above 
that temperature the vapor or gas cannot be liquefied by pres- 
sure alone. It has been proposed to call a substance which is 
above the critical temperature a gas, and one which is below a 
vapor. 

Experiments on liquids strongly heated in strong glass 
tubes show that vaporization proceeds gradually as the tem- 
perature rises, until a temperature is reached at which the line 
of demarcation between the liquid and its vapor becomes indis- 
tinct. Above that temperature the liquid all disappears, and 
the tube is full of gas. This is the critical temperature. 
Avenarius* by this method determined the critical tempera- 
ture of four liquids. He also selected from Regnault's experi- 
ments the data most applicable, and from them deduced 
equations like those given by Zeuner for the internal latent 
heat of vapors, and calculated the critical temperature by their 
aid. The results are as follows : 

Experimental. Calculated. 

Ether , I96°.2 C. I96°.8 C. 

Carbon bisulphide 276°.! 274".o 

Carbon tetrachloride 292°. 5 298°.7 

Aceton 246°. i 230°.4 

Effect of Pressure on Change of State. — If equation 
(128) be solved for the differential of the pressure with regard 
to temperature, 

dp _ r , . 

It-AiTr' ^'^^^ 

* Poggendorff's Annalen, cli. 1874. 



102 THERMODYNAMICS OF THE STEAM-ENGINE. 

in which A and T are positive, and r is positive below the 

dp 
critical temperature. Consequently -7- is positive or negative, 

dp 
according as s is greater or less than cr. When ~ is positive, 

an increase of pressure causes a rise of the temperature of the 
change of state, and vice versa. 

The application of the foregoing to the formation of steam 
only confirms what we already know, that the temperature of 
boiling-point increases with the pressure. But an application 
to the melting of ice is of more interest. To make the appli- 
cation, let s represent the specific volume of water, and cr that 
of ice, the latter being larger than the former. In this case u is 

dp . 
negative, and -t- is also negative, showing that an increase of 

pressure lowers the melting-point, a fact that has been proved 
by experiment, and which is used in explaining regelation. 

Curve of Constant Steam Weight. — It was formerly 
assumed in the theory of the steam-engine that the interchange 
of heat between the steam and the iron of the cylinder was by 
radiation ; and further, that the condensation accompanying 
adiabatic expansion formed a cloud which instigated a rapid in- 
terchange of heat, where before Httle had occurred. The steam- 
jacket was assumed to impart just heat enough to dissipate 
this cloud and keep the steam dry. Hence the curve of dry 
saturated steam was of great importance in the theory of the 
steam-engine, and it is sometimes drawn on indicator cards 
instead of the hyperbola. The substitution has no good 
reason, for the curve is not a better approximation to the 
curve drawn by an indicator, and is more troublesome to con- 
struct. 

The action of steam in the engine cylinder has been proved 
to be quite different, for the interchange of heat is caused by 
condensation by contact of the steam with the iron, or by 
evaporation of moisture from it, and the curve of saturated 
steam no longer plays an important part in the theory of the 



SATURATED VAPOR. IO3 

steam-engine. Still it is of importance as forming the bound- 
ary-line between superheated steam and wet steam. 

The curve may be represented very closely by an expo- 
nential formula resembhng that deduced for the adiabatic line 
for a perfect gas ; i.e., 

pv^ = p{o^ — zonsX. (136) 

Rankine proposed the value \^ for the exponent n^ and 
Zeuner has found that 1.0646 gives still a closer approximation. 
The actual curve may be drawn by plotting pressures and 
volumes from a table of the properties of saturated steam. 

Exponential Equation. — To find the exponent of an 
equation representing a curve passing through two points, a^ 
and a^ , Fig. 27, take logarithms of both sides 
of equation (136), and we have 

n log V -\- log p ^ n log v^ -\- log p^, 
n^-, , — - — (137) 

log V - log V, ^ ^'^ F,^. ,^. 

Isothermal Lines. — Since the pressure of saturated vapor 
is a function of the temperature only, the isothermal line of a 
mixture of a liquid and its vapor is a line of equal pressures, 
parallel to the axis of volumes. Steam expanding from the 
boiler into the cylinder of an engine follows such a line ; that 
is, the steam line of an automatic cut-off engine with ample 
ports is nearly parallel to the atmospheric line. 

The heat required for an increase of volume at constant 
pressure is 

Q = r{x,-x,), (138) 

which may be obtained by integrating equation (123) with the 
assumption that the temperature is constant, or it may be 
written directly, since r is the heat of vaporization, and x^ — x^ 
is the weight of liquid vaporized. 




104 THERMODYNAMICS OF THE STEAM-ENGINE. 

The work done by the vapor during such an expansion is 

W = p{v^ - v^ ^pu {x, - x). . . . (139) 

Isodynamic or Isoenergic Lines. — The following method 
of treating the isodynamic changes of a mixture of a liquid 
and its vapor is due to Zeuner, and is similar to his method of 
treating adiabatic changes. It does not give an equation to 
the curve of pressures and volumes, but it gives the solution of 
all problems that arise. 

The increase of intrinsic energy of the mixture of a liquid 
and its vapor, above freezing-point, is 

^ = ^(^ + ^P) (140) 

The change of intrinsic energy in passing from one condition 
to another is 

^. -^i = ;^fc-^i + -^2A--^A). . . (141) 

When the change is isodynamic, the energy remains the 
same by definition, and 

^. - ^1 + ^.P2 - -^iPi = o ;..... . (142) 

which equation, together with the formulae 

v^ = x^u^ + <r, V, — x,u^ + C7, ... (143) 

gives the means of solving all problems. 

For example, suppose that the initial and final pressures are 
given, to find the corresponding volumes ; then, x^ being also 
known, x^ may be found from equation (142), and then the 
volumes may be found by equations (143). On the other hand, 
if the volumes are given and the pressures are required, the 
problem can be solved only by approximations. 

Assume a probable value // for the final pressure, and cal- 



SATURATED VAPOR. I05 

culate the corresponding value of v^. From the comparison of 
v^ and 27/ assume a second approximate value//', and calculate 
v^\ and repeat the process till a sufficiently close approxima- 
tion is attained. For the first approximation it will commonly 
be convenient to assume that the pressures are inversely pro- 
portional to the volumes. 

The direct determination of the heat required and of the 
external work done by the mixture of liquid and vapor during 
an isodynamic expansion would require, for convenient work, 
the calculation of special empirical formulae or of the tables 
equivalent to them ; which is not justified by the importance 
of the subject. An approximate solution may be had by aid of 
an exponential formula determined from the initial and final 
pressures and volumes ; and since the curve represented by such 
a formula agrees quite well with the actual expansion curve, 
the approximation is sufficient for the solution of problems. 

Suppose we have the formula 

pv*" = p^v^ = const. ; 
then 

Q = AW= Ajpdv, (144) 

since the heat received is all changed into external work, the 
intrinsic energy remaining constant. 

Zeuner states that n is 1.0456 when the steam is dry and 
saturated at the initial state. 

Entropy of a Mixture of a Liquid and its Vapor.— 
From the second law of thermodynamics, 

a(p = ^ ; 

in which is the entropy, dQ is the heat transmitted, and T is 
the absolute temperature. Since the entropy depends only on 
the state of a substance, and not on the method of arriving at 
that state, the increase of entropy of one unit of weight of a 
given mixture of a liquid and its vapor, above the entropy of 



I06 THERMODYNAMICS OF THE STEAM-ENGINE. 

one unit of weight of that Hquid at freezing-point of water, 
may be calculated in the following method : 

Suppose that one unit of weight of a liquid be raised from 
freezing-point to the temperature t, and that a portion ;ir be then 
changed into vapor. During the first operation the increase of 
entropy will be 

e/o 1 t/o 1 

and during the second operation the increase will be 

xr 

since the heat is added at a constant temperature t during that 
operation. The entire increase of entropy will be 



nt cdt xr 



For any other state determined by x^ and t^ we shall have^ 
for the increase of entropy above that of liquid at freezing-point, 

^- + <^i • 

The change of entropy in passing from one state to another 
is 

XT X 7" 

0-0. = -:=. + ^-^-'+^.. . . . (145) 



Entropy of the Liquid. — When the specific heat of a liquid 
is known in terms of the temperature, the entropy of the liquid 
is readily calculated. Thus, for ether, the equation is 

= r (0.52901 + 0.00591 8/j^^. 



SATURATED VAPOR, lO/ 

The form of the equation for the entropy of water is more 
easily stated for a special case. For example, at 13° C, it is 

T T T 

i.(X>72 log,y-+ 1.0044 log. 7^+ 1. 00 1 6 log,-^ — 0.04663. 

Adiabatic Equation for a Liquid and its Vapor. — 

During an adiabatic change the entropy is constant, so that 
equation (145) gives 

^^+^. = T'+^, (146) 

When the initial state, determined by x^ and t^ or /, , is 
known and the final temperature t^ , or the final pressure p^ , 
the final value x^ may be found by equation (146). The initial 
and final volumes may be calculated by the equations 

v^ = x^r^ -\- (J and v^ = x^r^ -{- (T. 

Tables of the properties of saturated vapors commonly give the 
specific volume j, but 

Problems in which the initial condition and the final tem- 
perature or pressure are given, may be solved directly by aid 
of the preceding equations. Those giving the final volume in- 
stead of the temperature or pressure can be solved only by 
approximations. An equation to an adiabatic curve in terms of 
/ and V cannot be given, but such a curve for any particular 
case may be constructed point by point. 

Clausius and Rankine independently and at about the same 
time deduced equations identical with equations (145) and (146), 
but by methods each of which differed from that given here. 

If tables giving 6, the entropy of the liquid, are not at hand, 
an approximate result may be obtained by considering the 
specific heat ^ to be a constant, so that 



6 = J ^-^=cj -^ = c\og, 



— r \r\CT - 

T 



I08 THERMODYNAMICS OF THE STEAM-ENGINE. 

or equation (146) may be written, 

^ = ^i + log.|f (147) 

In the discussion of the specific heat A of a saturated vapor, 
it appeared that the expansion of dry saturated steam in a non- 
conducting cyHnder would be accompanied by partial conden- 
sation. The same fact may be brought out more clearly at 
this place. One pound of dry steam at 100 pounds absolute 
pressure will have the values 

^x = 327°.58 F., r, = 884.0, 6>, = 0.4733, x,= \. 

If the final pressure is 15 pounds absolute, we have 

^, = 2I3°.03 F., ^ = 965.1, 6^, = 0.3143; 

whence 

884.0 , 965. 1 ;r, , 

6^8 + 0.4733 =^6:^3- + 0.3143; 

.'. ^, = 0.8133. 

On the other hand, h is positive for ether, and partial con- 
densation takes place during compression in a non-conducting 
cylinder. For example, let the initial condition be 

t^ = 10° C, r, = 93.12, 0^ = 0.0191, X, = I, 

and let the final conditions be 

t^ = 120° C, r^ = 72.26, 6^ = 0.2045, 



then 



93.12 , 72.26;r2 , 

+ 0.0191 = + 0.2045 ; 



283.7 393.7 

and ' ^^ = 0.724. =v^ 

Equation (146) applies to all possible mixtures of a liquid 
and its vapor, including the case of ;fj = o or the case of liquid 



SATURATED VAPOR. 



109 



without vapor, but at the pressure corresponding to the tem- 
perature according to the law of saturated vapor. When 
appHed to hot water, this equation shows that an expansion in 
a non-conducting cyHnder is accompanied by a partial vapor- 
ization. 

There is some initial state of the mixture such that the 
value of X shall be the same at the beginning and at the end, 
though it may vary at intermediate states. To find that value 
make x^ = x^ in equation (146) and solve for x^ , which gives 



- 6'„ 



^ 
T. 



(148) 



The value'of x^ to fulfil the conditions given varies with the 
initial and final temperatures chosen, but in any case it will not 
be much different from one half. It may therefore be generally 
stated that a mixture of steam and water, when expanded in a 
non-conducting cylinder, will show partial condensation if more 
than half is steam, and partial evaporation if more than half 
water. If the mixture is nearly half water and half steam, the 
change must be investigated to determine whether evaporation 
or condensation will occur ; but in any case the action will be 
small. 

Construction of Adiabatic Lines. — In case a series of 
adiabatic lines is to be drawn, the following method may be 
used with advantage. In Fig. 28 
draw the line BB parallel to OP, p 
the axis of P, making OB = cr, so 
that BB represents the volume of 
one kilogram of water at all tem- 
peratures and pressures. At the 
point O, which represents the high- 
est pressure to be used, draw °^ 
OD =z u^ , corresponding to the 
given pressure ; then D represents the condition when the mix- 
ture is all dry saturated steam; i.e., x ^ \, v ^=^ s. Though not 



B 




\ 


D 





\ 


\^=1. 




\ 


\ 




^-0^^==-:===^ 


X' 


B 


I'o 


^1 


v=s 


t) u' 


V 



Fig. 28. 



no THERMODYNAMICS OF THE STEAM-ENGINE. 

essential to the solution of the problem, it is interesting to draw 
the line of saturated steam DD, which forms a boundary be- 
tween moist steam and superheated steam ; a point to the left 
of DD, or between that line and BB, represents a mixture of 
water and steam, and a point to the right of DD represents 
superheated steam. 

The points O and D represent the two extreme cases, pure 
water and dry steam ; and the point x^ , between O and />, repre- 
sents a niiixture of water and steam. Equation (154) gives for 
a pressure p the following expressions for x^ , x^ and x' , corre- 
sponding to the initial conditions O^ x^ , and i^ or ;i: = i : 

^+^ = ^.; (149) 

-f + ^-^^ + ^.i .... (150) 

XT T 

T + ^=7t + ^'- • • • • ('50 

Subtracting in succession equation (149) from (150) and 
(151), we have 

r _ vl - -!J-. 

\X Xq) y^ jtTj ™ , 

f T 

' \^ -^0 j 'nr ~~ y > 

•■•Z3-j. = ^. (152) 

Designating the final volumes by v^, v, and v\ we have 

V^ = X^U -\- C, V =^ XU -{- (T, v' =z x'u -(- (7 ; 
V — V^ X — x^ 



':; .... (153) 

^ V ^x,{y' -v^-^v, (154) 



SATURATED VAPOR. Ill 

Now calculate x^ and x' with the corresponding values of v^ 
and v^ in the usual method, and calculate v by the equation 
(154), and complete Fig. 28 by plotting the points x^, x, and x' 
on the line x^ at a distance v^x^ from <?z', equal to the pres- 
sure/. 

The equations (149), (151), and (154) are true for any press- 
sure p ; for example, the pressure represented by the dotted 
line on Fig. 28, so that a sufficient number of points may be 
located and the three curves ox^ , x^x, and Dx' may be drawn. 

Thus far it appears that the labor of constructing the inter- 
mediate curve x^x directly by the usual method would be less, 
but an advantage will be given by the new method when a 
large number of intermediate curves corresponding to different 
initial values of x are to be drawn; equation (153) will then 
give the several values of x with great rapidity. Fig. 28 is also 
useful in giving a comprehensive idea of the action of various 
mixtures of water and steam in a non-conducting cylinder, the 
proportions being as nearly correct as can be represented by a 
figure of the size. 

External Work during Adiabatic Expansion. — Since no 
heat is transmitted during an adiabatic expansion, all of the 
intrinsic energy lost is changed into external work, so that, by 
equation (141), 

W=E,- E,=: ~ {q, - ^, + x,f>, - x,p,j. . (155) 

The adiabatic curve cannot be well represented by an ex- 
ponential equation ; for if an exponent be determined for such 
a curve passing through points representing the initial and final 
states, it will be found that the exponent will vary widely with 
different ranges of pressure, and still more with different initial 
values of x ; and that, further, the intermediate points will not 
be well represented by such an exponential curve, even though 
it passes through the initial and final points. 

This fact was first pointed out by Zeuner, who found that 
the most important element in determining n was x^ , the ini- 
tial condition of the mixture. He gives the following empirical 



112 THERMODYNAMICS OF THE STEAM-ENGINE. 

formula for determining n, which gives a fair approximation for 
ordinary ranges of temperature : 

;2 = 1.035 + O.I 00;ir, (l5^) 

Rankine* proposed the exponential formula 
piN- = const. 

for the expansion of saturated steam in a lagged cylinder with- 
out a steam-jacket. 

It is probable that this equation was obtained by comparing 
the expansion lines on a large number of indicator diagrams. 
It corresponds nearly with the true adiabatic line for x^ , the 
initial value at cut-off, equal to 0.80. This equation has been 
largely used in England on account of the esteem in which 
Rankine's work is held ; and as he does not state its origin, it 
appears to have been regarded as the true adiabatic line for a 
steam-engine. 

There does not appear to be any good reason for using an 
exponential equation in this connection, for all problems can be 
solved accurately by the method given, and the action of a 
lagged steam-engine cylinder is far from being adiabatic. An 
adiabatic line drawn on an indicator card is instructive, since it 
shows to the eye the difference between the expansion in an 
actual engine and that of an ideal non-conducting cylinder ; but 
it can be intelligently drawn only after an elaborate engine 
test. For general purposes the hyperbola is the best curve for 
comparison with the expansion curve of an indicator card, for 
the reason that it is the conventional curve, and is near enough 
to the curve of the diagrams from good engines to allow a prac- 
tical engineer to guess at the probable behavior of an engine, 
from the card alone. It cannot in any sense be considered as 
the theoretical curve. 

EXAMPLES. 

I. Calculate the pressure, heat of the liquid, total heat, 
heat of vaporization, specific volume, etc., at several tempera- 

* Steam-engine and Other Prime Movers. 



SATURATED VAPOR. II3 

tures for the vapors for which the data and equations are given, 
and compare with results given in the Tables of the Properties 
of Saturated Steam. 

2. Find the exponent for an exponential curve passing 
through the points / = 30, 7^ = i .9, and /^ = 1 5, 7/ = 9.6. 

3. Find the exponent for a curve to pass through the points 
p = 40, z' = 2, and /j := 12, ^1 = 6. 

4. In examples 2 and 3, let / be the pressure in pounds 
on the square inch, and v the volume in cubic feet ; find the 
external work of expansion in each case. 

5. Find the external work of expansion of a fluid, following 
the law given by the equation /z/s ^ which has the initial volume 
3 cubic meters, and the initial pressure 4 atmospheres, and 
which expands till the pressure becomes one atmosphere. 

6. A pound of steam and water at 150 pounds pressure is 
0.6 steam ; what is the increase of entropy above that of water 
at 32° F. ? 

7. A kilogram of chloroform at 100° C. is 0.8 vapor ; what is 
the increase of entropy above that of the liquid at 0° C. ? 
Apply to other vapors for which data are given. 

8. The initial condition of a mixture of water and steam is 
t = 320° F., ;ir = 0.8 ; what is the final condition after adiabatic 
expansion to 212° F. ? Solve with the following values for x: 
0.9, 0.6, 0.4, 0.3, 0.0. 

9. The initial condition of a mixture of steam and water is 
p = 3000 mm., X = 0.9 ; find the condition after an adiabatic 
expansion to 600 mm. Apply to other vapors for which data 
are given. 

10. A cubic foot of a mixture of water and steam, x = 0.8, 
is under the pressure of 60 pounds by the gauge. Find its 
volume after it expands adiabatically till the pressure is reduced 
to 10 pounds by the gauge ; also the external work of expansion. 

11. A test of an engine with the cut-off at 0.106 of the 
stroke, and the release at 0.98 of the stroke, and with 4.5 per 
cent clearance, gave for the pressure at cut-off 62.2 pounds by 
the indicator, and at release 6.2 pounds ; the mixture in the 
cylinder at cut-off was 0.465 steam, and at release 0.921 steam. 



114 THERMODYNAMICS OF THE STEAM-ENGINE. 

Find (i) condition of the mixture in the cyHnder at release on 
the assumption of adiabatic expansion to release ; (2) condition 
of mixture on the assumption of hyperbolic expansion, or that 
pv=^p^v^\ (3) the exponent of an exponential curve passing 
through points of cut-off and release ; (4) exponent of a curve 
passing through the initial and final points on the assumption 
of adiabatic expansion ; (5) the piston displacement was 0.7 
cubic feet, find the external work under exponential curve 
passing through the points of cut-off and release; also under the 
adiabatic curve. 



CHAPTER VIII. 

SUPERHEATED STEAM. 

A DRY and saturated vapor, not in contact with the Hquid 
from which it is formed, may be heated to a temperature 
greater than that corresponding to the given pressure for the 
same vapor when saturated. Such a vapor is said to be super- 
heated. When far removed from the temperature of satura- 
tion, such a vapor follows the laws of perfect gases very nearly, 
but near the temperature of saturation the departure from 
those laws is too great to allow of calculations by them for en- 
gineering purposes. 

In the case of superheated steam various provisional char- 
acteristic equations have been proposed for use until the neces- 
sary experimental investigation shall give the data for a true 
theory. The theory given here was proposed by Zeuner. It 
is convenient for calculation and appears to give good results. 

Substituting in the characteristic equation for a gas 

pv = RT, 
the value of R from equation (6i) gives 

^^ = ^-^=i-^r-- ^- • • ('57) 

The form of characteristic equation proposed by Zeuner for 
superheated steam is 

P^^\- ^- • T-Ct^ (158) 

"5 



ii6 



THERMODYNAMICS OF THE STEAM-ENGINE. 



The Specific heat at constant pressure Cp is assumed to be 
constant, y^ is a constant suggested by the ratio k of the specific 
heats of a gas ; but it will be shown that the specific heat at 
constant volume, determined from the equation (158), is a 
variable, consequently k cannot be the ratio of the specific heats 
of superheated steam. C and a are constants that are to be 
determined from the known properties of saturated and super- 
heated steam. 

Partial differentiation of equation (158) gives 






Apk 



Cp{k- I)' 



Avk ap"--^AkC 



+ 



Cp{k — l) Cp{k — i) 



(159) 
(160) 



Application of the First Law. — The application of the 
first law of thermodynamics by aid of equation (48), 



A ( \dp 



/^\ (dn\ I _ 



gives another form for f-^- . Substituting for o and n in terms 
\dpl ^ 

of the specific heats gives 



d 



dt\ 

^''\dv)^_ 



.''(1),? 



dv 



t-^A. 



(161) 



Substituting the value of (--— J from equation (159), and per- 



\dv 
forming the differentiation indicated. 



Ak 



d 



c ^^] 

\dpi ^Ap _ 

dv 



d 



dt 

~d. 

dv 



'"^^dpL^^ 



= A: 



A 



(162) 



SUPERHEATED STEAM. WJ 

Integration gives 

Application of the Second Law. — Equation (55), 

'.-'— (5).(*l 



deduced by the successive application of the two laws of ther- 
modynamics, can be most conveniently used in this place. 
Substituting the values of the partial differential coefficients 
from equations (159) and (163) gives 

- (^ - I)" T 
cp-c,- cpc, ^ ^^^ ; 

.-. -^=l-\-C^- 7-^.-7—-, . . . (164) 

c^ ^ ^ k Apv ^ ^' 

which gives the method of calculating the specific heat at con- 
stant volume when Cp and k are known. 

Value of the Exponent a. — Equating the values of the 
differential coefficient given by equations (160) and (163), 
Av Avk ap'^-^AkC 



c,(k— I) cp{k- I) c^(k— I) • 

Substituting for C from equation (158), and for c^ from (164), 
we have 

Av V {k - ly ^"1_ Avk 

c^k - I) L^ + ^^ 'k • ~Afv\ ~ ~^Jk~'^~T) 

a p'^-'Ak Vcp k - I T V ~\ 
+ 5(/^ - I) \lA ' ~F~ • y ~/^^J ' 

Av , k—\ T Avk , T aAvk 



' Cp{k — \) . k ' p Cp(k — i) ' p Cp{k — i) ' 
k— I ^ ^ _ ^ ^ ^ . 

k ' p Cp ~ p Cp ' k— \' 



Il8 THERMODYNAMICS OF THE STEAM-ENGINE. 

Characteristic Equation. — Substituting the value deduced 
for a in equation (158) gives, for the characteristic equation for 
superheated steam, 

/^ = J-'^. T-Cp^ (166) 

Thermal Capacities. — From equations (11), (159), and 
(164), 

/- fe_ \{^ - (^ - 0' JL ^/^ 

^ - ^^ V, ^)\dv]^ ~ ''^''^ k ' Apv' elk - I) ' 

... i^dk-i)'^ (167) 

From equations (15), (163), and (164), 

'cp \(dt\ {k - ly T Av 



— m = c,, 



— I 

~k~ p 



'Apv ' c,{k - i)' 

k-iT , ^„, 

m = Cp — 7 — (168) 



From equations (17) and (160), 
idt\ Apk 

o = c,[-^)^ = r:r, • • (^69) 

From equations (18) and (163), 

ldt\ Av . . 

n = c.[^)^ = Y=ri (^70) 

General Equations. — Substituting the values of /, m, n^ 
and in equations (5), (6), and (7) give, for the general equations 
for superheated steam, 

dQ= c\dt-\-{k-i)^dv\', . . (171) 
dQ= cp[dt-^^ .jdpy, . . (172) 
dQ=-^^—^\vdp+kpdv\ (173) 



SUPERHEATED STEAM. II9 

It is instructive to compare these equations with the gen- 
eral equations (70), (71), and (72) for perfect gases, which may 
be written, 

dQ= c^^dt + {K-i)^dv]; . . (174) 
dQ=-. c,[d^-^-jdp]; . . (175) 

dQ = -^^--^[vdj> + Kpdv^. .... (176) 

To obtain equation (176), equation (72) may be written, 

v p 

dQ = c^-^dp-\-Cp^dv\ 

Ac^v AcpP 
. • . dQ = \ — dv. 



It is to be remarked that equation (174) is not useful in its 
present form, since c^ is a variable, but it is written for symme- 
try in comparison with equations (174), (175), and (176). 

Entropy. — Equation (172) gives 

,^ dQ \dt k-\dp\ . ^ 

( T k — \ p ) 

.-. 0- 00 = ^/jiog,^ J~^^^^j\^ ' (^78) 

which is to be compared with equation (85) for gases. Equa- 
tions in terms of v and t', or p and v may be deduced, which 
will also have the same form as those for gases. 

Value of k. — The characteristic equation for superheated 
steam is intended to apply to all degrees of superheating, ap- 
proaching, at one limit, the condition of a gas, and at the other, 



I20 THERMODYNAMICS OF THE STEAM-ENGINE. 

that of saturated vapor. For a mixture of a liquid and its 
vapor we have, from equation (145), 

ixr\ c 
<^0 = d\--^\-^-j.dty 

or, for saturated steam with x ^= \, 

d(f)^^dt-^d\~)^~ [cdt + dr — Y dt^- • (i/Q) 

Equations (177) and (179) should both be true for dry sat- 
urated steam, whence 

/ k- I T dp\ dr r , ^ , 

'A'~-^-'j'dt)-'+^-T- • (^^^) 

By equation (127) the right-hand member of equation (180) 
is equal to h, the specific heat of saturated steam ; consequently 

p ' dt'^^ 

Numerical Values. — Regnault gives as the results of three 
experiments on the specific heat of superheated steam at con- 
stant pressure 

0.481 1 1, • 0.48080, 0.47963, 

and for the mean value 

Cp = 0.4805. 

With this value of Cp and the known values of the other 
factors, determined from the properties of saturated steam, the 
following values of k were calculated : 

Pressure, pounds ) 

4.1, - [ 5 '50 100 200 300 

on the sq. m. j -^ -' ^ 

^ 1.335 1-332 1.330 1.324 1. 316 



SUPERHEATED STEAM, 121 

Zeuner assumed for the constant k the value 

>^ = 1=1.333+, (182) 

which may be compared with the ratio of the specific heats of 
air, 

K — 1.405. 

With this assumed value of k and the known values of A 
and Cp the coefficient of T in the characteristic equation (166) 
becomes: 

c k — \ 
French system, ~ — r — = ^5 = 5 1.28 ; 

English system, ~ — 7 — — B = 93.46. 

The specific volume of saturated steam under atmospheric 
pressure and at boiling-point is 26.60 cubic feet or 1.661 cubic 
metres. Solving equation (166) for (7, 



p k 



and therefore we have- 
French system, 



51.28 X 373-7 - 10333 X 1.661 

c = 1 = 19^4 J 

10333* 

English system, 

93.46 X 672.7 — 2116.32 X 26.60 
2116.32'' 

Substituting the constants in the characteristic equation, 
gives — 

French system, pv = 51. 37^— 198/^ (183) 

English system, /z/ == 93.5 7" — 971/i (184) 



122 THERMODYNAMICS OF THE STEAM-ENGINE. 

Zeuner's constants for equation (183) differ from those given, 
since he used 424 for the mechanical equivalent of one cal6rie, 
and 273 for the absolute temperature of freezing-point, in this 
connection and in calculating his tables for saturated steam. 

In using these equations for superheated steam it is to be 
remembered that the pressures are specific pressures, i.e., kilo- 
grams per square meter or pounds per square foot, whereas the 
pressures of saturated steam are commonly stated in milli- 
meters of mercury or in pounds on the square inch. 

Specific Heat at Constant Volume. — The specific heat of 
superheated steam at constant volume may be calculated by 
applying equation (164) to the case of saturated steam. The 
following table gives the values obtained at several pressures : 

SPECIFIC HEAT OF SUPERHEATED STEAM. 

Pressures, pounds \ ^ ^^ ^^^ ^^^ ^^^ 

. , r 5 50 100 200 300 

per square mch, ) 

Specific heat, ^^ , 0.351 0.348 .346 .344 .341 

This table develops the fact already mentioned, that the 
specific heat of superheated steam at constant volume, deduced 
from the form of the characteristic equation (166) and the 
known properties of saturated and superheated steam, is a 
variable. This conclusion applies properly to steam that is only 
slightly superheated, whereas our experimental knowledge of 
the properties of superheated steam relates to steam that is 
superheated to a marked degree. It is quite as reasonable to 
suppose that the specific heat at constant volume is constant, 
as to suppose that the specific heat at constant pressure is con- 
stant, as has been assumed. Had the specific heat at constant 
volume been assumed to be constant, and had the character- 
istic equation been assumed to have the form 

pv = BT— Cv-\ 

then the specific heat at constant pressure would have appeared 
to be variable. A complete set of equations could be worked 



SUPERHEATED STEAM. 1 23 

out under such an assumption that would be on as good a basis 
as those we have deduced. The form that has been deduced 
appears to be more useful in engineering work where the pres- 
sures are more commonly given than the volumes. 

Intrinsic Energy. — The combination of the equation 

dQ = A{dE-\-pdv) 

with equation (173) gives 

dE = j^^ {vdp + pdv) = ^i— 4/^). 

.-. E-E, = j^^{pv-p,v,) (185) 

In this equation it may be assumed that E^ is the increase 
of intrinsic energy of saturated steam at atmospheric pressure, 
above that of water at freezing-point. From equation (140), 

^^« == ^0 + Po ; 

hence the increase of intrinsic energy of superheated steam, 
having the pressure/ and the volume v, above that of water at 
freezing-point, is 

Taking the values of q^, p^.p^, and v^ from the tables of the 
properties of saturated steam at boiling-point, we have — 

French system, ^ — h _ /^ + 47^-^ I (186) 

English system, ^ = T /^ + 857.2 (187) 

Total Heat. — By total heat of superheated steam is meant 
the heat required to change one unit of weight of water at 



124 THERMODYNAMICS OF THE STEAM-ENGINE. 

freezing-point into superheated steam having a given tempera- 
ture and pressure. It may be divided into the heat equivalent 
of the intrinsic energy and the heat equivalent of the external 
work. The first part may be calculated by equation (i86) or 
equation (187). The second part maybe assumed to be 

Apv. 

Using the same character that has been used for the total 
heat of saturated steam, 

vp -\- Apv -\- const. ; 



k-\ 



Ak 



. • . 'K. = T 'Vp -\- const. 

Substituting forpv from equation (166) 

X = c^(^T--^p'-T^)+ const., . . . (188) 

or replacing the constants hy their known values, we have — 

French system, A = 0.4805 {T — 3.86/^) + 476.2 ; . . (189) 

English system, X — 0.4805 {T — 1.038/^) -|- 857.2. . . (190) 

Comparison with Experiments. — Experiments on the 
specific volume of superheated steam were made by Hirn,"^ 
from the report of which Zeuner selected the experimental data 
in the following table. The specific volume has been calculated 
by aid of equation (183), and placed in the table opposite the 
experimental results to show the comparison of the character- 1 
istic equation with experiment. 

*Theorie Mecanique de la Chaleur. 



SUPERHEATED STEAM. 
SPECIFIC VOLUME OF SUPERHEATED STEAM. 



125 



Pressure 

in 

atmospheres. 


Temperature. 
Centigrade. 


Specific Volume. 
Cubic meters. 


Hirn's 
experiments. 


Equation (183). 


I 

I 
3 
4 
4 
4 
5 
5 


118. 5 

141 

200 

165 

200 

246 

162.5 

205 


1.74 

1.85 

0.697 

0.4822 

0.522 

0.5752 

0.3758 

0.414 


1.75 

1.87 

0.699 

0.476 

0.520 

0.577 
0.376 
0.418 



The following table shows that the characteristic equation 
for superheated steam applies fairly well to the limiting case of 
saturated steam. The values in columns 2 and 4 were taken 
directly from the tables of the properties of saturated steam, 
and those in column 6 were calculated in the usual manner for 
saturated steam with ;tr = i. The specific volumes in column 
3 were calculated by aid of the empirical equation for the tem- 
peratures and pressures taken from tables for saturated steam. 
Columns 5 and 7 were calculated by equations (184) and (178). 
The latter equation gives a negative change of entropy for 
saturated steam for increasing pressure, which is to be taken 
from the entropy of steam at freezing-point. 

APPLICATION OF EQUATION (184) TO SATURATED STEAM. 



Absolute 
pressure, 


Specific Volumes, 
Cubic feet. 


Total Heat. 


Entropy. 


pounds 














per 
square 


Tabular 


Equation 


Tabular 


Equation ' 


Equation 


Equation 


inch. 


value. 


(184). 


value. 


(190) 


(145). 


(178). 


I 


2 


3 


4 


5 


6 


7 


14.7 


26.60 


26.6 


I146.6 


1146.6 


1.7484 


1-752 


30 


13-59 


13.7 


II58.3 


1158.4 


I. 6891 


1.704 


60 


7.096 


7.12 


II71.2 


1171.0 


1.6340 


I 641 


100 


4.403 


4.38 


I181.9 


1180.3 


1-5945 


1.598 


150 


3. on 


3.00 


II9I.2 


1190.2 


I . 5649 


1.568 


200 


2.294 


2.30 


II98.4 


1198.5 


I . 5446 


1.546 


300 


1.554 


1.57 


1209.3 


1207.2 


1.5262 


1. 517 



126 THERMODYNAMICS OF THE STEAM-ENGINE, 

Adiabatic Line. — Since the entropy remains constant 
during an adiabatic change, equation (178) gives 

£=©- • <"■) 

This equation has of course the same form as the corre- 
sponding one for a gas, with the essential difference that k is 
an arbitrary constant, while k is the ratio of the specific heats. 
Equations may also be deduced in terms of p and v^ or T and 
V, i.e., 

v^p — v^p^ — const., . . . . (192) 

r^^-^ z= ry-^ = const (193) 

During an adiabatic expansion, in which external work is 
done at the expense of the intrinsic energy, the degree of super- 
heating is reduced, and if the expansion be carried far enough 
the vapor becomes saturated, and then moist. In such case 
the equation 



■^ 1 

or 



e. 



1^ + ^, + 0.4805 log, -^ = ^+^. . . (194) 

is taken. 

For example, let the initial pressure be lOO pounds absolute 
per square inch, and the initial temperature be 400° F. ; re- 
quired the condition of the steam after an adiabatic expansion 
to 15 pounds absolute. Here we have 

t, = 327°.6, r, = 884.0, e^ = 0.4733, 
/, = 2i3°.o, r, = 965.1, 6*^ = 0.3143; 

884.0 , . ^ , 860.7 965.i;ir, , 

■-■ jm+ 0.4733 + 0.4805 log. ^g- = ^^- + 0.3 143 ; 

. • . X = 0.923. 



SUPERHEATED STEAM. I27 

Isodynamic or Isoenergic Line. — The equation to this 
line is obtained from equation (18$) by making E equal to E^ , 
so that 

/^=A^^« -const (195) 

The isodynamic line for superheated steam, like that for a 
gas, is a rectangular hyperbola. 

The combination of equation (195) with the characteristic 
equation gives 

BT-Cp^^BT,-Cp^, 

from which it is evident that the isodynamic line for super- 
heated steam differs from the isothermal. 

The external work during an isodynamic change is 

W = fpdv = p,v, log, -f- = p,v, log, ~. . (196) 

Since all the heat applied is expended in external work, 

Q = AIV. (197) 

Isothermal Line. — The equation to the isothermal line is 
obtained from the characteristic equation by making T con- 
stant, so that 

/^=A^i- ^(/^-A*) (198) 

The heat applied during an isothermal change is obtained 
by integrating equation (172) with Z constant ; 

••• e=^^>^i°g'7; (199) 

We have also 

Q==A{E,-E,+ W). 



128 THERMODYNAMICS OF THE STEAM-ENGINE. 

Hence the external work is 

or by aid of equation (185) we have 

T T^ J^ 

^=-^.log.^] + 3(A^. -A^»)- • . (200) 

EXAMPLES. 

1. What is the weight of one cubic foot of superheated 
steam at 500° F. and at 60 pounds pressure absolute ? 

2. Superheated steam at 50 pounds absolute has half the 
density of saturated steam at the same pressure. What is the 
temperature? 

3. Find the increase of intrinsic energy and increase of en- 
tropy of a pound of superheated steam at 100 pounds absolute 
and at 400° F., above the values at 32° for water. 

4. Find the external work of one kilogram of steam in ex- 
panding adiabatically from the pressure of 3000 mm. of mer- 
cury, and the temperature 300° C. to the pressure of 2000 mm. 
Find also the final temperature and volume. 

5. In Example 4 find the external work for an isothermal 
expansion from the initial condition to the final volume as 
determined in that example. 

6. Let the initial temperature of superheated steam be 380° 
F. at the pressure of 150 pounds absolute; find the condition 
after an adiabatic expansion to 20 pounds absolute. Determine 
also the initial and final volumes. 

7. In Example 11, page 113, suppose that the steam at 
cutoff were superheated 10° F. above the temperature of satu- 
rated steam at the given pressure, and solve the example. 



Pi 



TLZVi 



CHAPTER IX. 

FLOW OF FLUIDS. 

Let Fig, 29 represent two communicating cylinders, each 
of which is provided with a piston moving without friction ; on 
one the constant pressure p^ is exerted, and the other moves 
against a less pressure p^. The ori- 
fice of communication C is so rounded 
that there is no contraction, and the 
fluid friction is considered to be so 
small that it may be neglected. The ^ '^^' 

two cylinders are supposed to be filled with a fluid which flows 
from A into B under a constant difference of pressure /^ — p^, 
and the problem is to find the velocity of flow and the weight 
or volume of the discharge per unit of time. 

At and near the orifice there will be a commotion or rapids, 
which will in general prevent us from knowing the condition 
of the fluid at that point, but it may be assumed that at a suffi- 
cient distance in front of and beyond the orifice the fluid is in 
equilibrium, and that we may apply the deductions of thermo- 
dynamics, without serious error, to the fluid in the cylinders 
A and B. 

It will be supposed that the cylinders themselves are non- 
conducting, but that the quantity of heat Q is supplied to each 
unit of weight passing through the orifice ; Q may be zero or 
negative, in which last case heat is withdrawn. 

The work done 07t each unit of weight of fluid by the piston 
in A, in forcing it through the orifice C, is p^v^ ; the work done 
dy the same fluid on entering the cylinder B, on the piston in 
that cylinder, is p^v^ . The gain of work by the fluid is there- 
fore 

p,V, - P,2J, . 

129 



I30 THERMODYNAMICS OF THE STEAM-ENGINE. 

If the intrinsic energy of a unit of weight of the fluid in 
A is £^, and of that in B \s E^, the energy changed into me- 
chanical work is 

to which is to be added the mechanical equivalent of the heat 
applied, or 

Q 

a' 

Now the gain of kinetic energy of motion, if the velocity 
changes from w^ in A to w^ in B, will be, for each unit of weight 
of fluid, 

Assuming that all of the work applied produces change of 
velocity only. 



2^ 2^ 



2 + ^i--^2 + A^i-A^.- • • (201) 



Incompressible Fluids. — The change of volume of most 
liquids under pressure is so small that it may be neglected, in 
which case the change of temperature may also be neglected 
and the intrinsic energy may be assumed to be constant. 

Making Q = o, the equation (201) reduces to 

-^-^-(A-AK, (202) 

since v^ = v^. If the velocity in A is small compared with that 
in B, we may suppress the subscript and write 



w 

— = (a-aK, (203) 

^,5 



FLOW OF FLUIDS. I3I 

which is the usual equation given in hydraulics. If the differ- 
ence of pressure is due to a difference of level, or head, h, we 
have 

in which y is the density, equal to — , so that 



w' 



2^=^ (204) 

Flow of Gases. — The most important case for gases is 
flow without transmission of heat — that is, an adiabatic flow ; 
in which case Q becomes zero. Equation (84) gives 

E= ^^ 



K— I 

so that equation (201) reduces to 









Usually the initial velocity is zero, in which case the sub- 
script may be dropped, and we may write 

W" K 

For an adiabatic transformation 



132 THERMODYNAMICS OF THE STEAM-ENGINE. 

The characteristic equation for gases, and the application 
to it of the first law of thermodynamics, give the two equations 



.\p{v. 



K — I 



/i^i 



^P CvT, 



Cp — c^ A. 



Again, 



2g A 






[-©-]■ 



(208) 



so that 






(209) 



If the area of the orifice is F, then the weight of air dis- 
charged per second is 

Fw 



G = 



^2 



or, substituting for w its value from equation (207), 



_ 77 ) ^^P 



G = F 






3 ^i^if ) 



% 



or, substituting for v^ its value 



(?:)-• 



i±i ) i 



O'AmXm-'^rv- ■ <-' 



Now G will be a maximum when 



FLOW OF FLUIDS. 133 



'A\. /A 



a)-"-©" 



le 



is a maximum. Differentiating and equating the first differen- 
tial coefficient to zero gives after reduction 

A I'^+iJ 

Putting for k its value 1.405, gives for the ratio of pressures 
producing the maximum flow 

A 

^^ = 0.5274. 

The equations deduced for the flow of gases can properly 
be applied only to the flow from one tube into another of 
smaller diameter when the specific pressure (or, as a substitute 
therefor, the specific volume, or the temperature) in the smaller 
tube is known, as well as the initial condition in the large tube. 
In making experiments on the flow of gases and vapors, it has 
been customary to allow the fluid in the tube to discharge into 
the atmosphere or into a reservoir, and to assume that the pres- 
sure in the tube is the same as that in the reservoir: and when 
the lower pressure is less than half the upper pressure such ex- 
periments with that assumption show an actual flow greater 
than the calculated flow and often very much greater. 

It was first suggested by Mr. R. D. Napier, in connection 
with experiments made by him on the flow of steam, that the 
pressure in the small tube is not necessarily the pressure of 
the atmosphere or of the reservoir into which it delivers; he 
further suggested that the pressure in the tube is never less 
than that pressure which gives a maximum flow. 

Professor Fliegner"^ found that the pressure in the throat 
of a well-rounded orifice through which air is flowing is never 
less than 0.57 of the absolute pressure in the reservoir from 
which the flow takes place. The mean of a large number of 



* Der Civilingenieur, vol. xx. p. 14. 1874. 



134 THERMODYNAMICS OF THE STEAM-ENGINE. 

experiments with two well-rounded orifices, 4.085 and 7.314 

mm. in diameter at the throat, showed that when the pressure 

in the reservoir was more than double the pressure of the air, 

the pressure in the throat was 0.5767 of the pressure in the 

reservoir. The pressure in the reservoir varied from 3366 mm. 

of mercury to 808 mm. The number 0.5767 is very nearly equal 

I 
to ~T^, and is to be compared with the ratio for maximum flow 

given above. In equation (210) substitute for v^ its value from 
the equation 

and we have 

in which k = 1.405 and — = 0.5767 ; 

.-. G = 0.4822 F\h^ . -4= . 

For the flow into the atmosphere from a reservoir having a 
pressure less than twice the atmospheric pressure, Fliegner 
found the empirical equation 



^ = 0.5622 ir^yA(A- A) 



T. 



These equations were found to be justified by a comparison 
with experiments on the flow of air, made by Fliegner himself, 
by Zeuner and by Weisbach. 

Although these equations were deduced from experiments 
made on the flow of air into the atmosphere, it is probable that 
they may be used for the flow of air from one reservoir into 
another reservoir having a pressure differing from the pressure 
of the atmosphere. 



FLOW OF FLUIDS. 1 35 

Fliegner's Equations for Flow of Air. — Introducing the 
values for g and R in the equations deduced by Fliegner, we 
have the following equations for the French and English sys- 
tems of units : 

French Units. 

Pr 

/,>2/«, 6^ = 0.395/^-;^; 



p,<2p,, G = o.7goF 



/ Pa{p.- Pa) 



English Units, 
p, > 2A, G = 0.530 i^-;^; 



A<2A, G^i.oeoF /^^^^^"^^^ 



/ 



/j = pressure in reservoir ; 
p^ = pressure of atmosphere ; 

7", = absolute temperature of air in reservoir; degrees centi- 
grade, French units ; degrees Fahrenheit, English units. 

In the English system/, and p^ are pounds per square inch, 
and F is the area of the orifice in square inches, while G is the 
flow of air through the orifice in pounds per second. If desired, 
the area may be given in square feet and the pressures in pounds 
on the square foot, as is the common convention in thermo- 
dynamics. 

In the French system G is the flow in kilograrhs per second. 
The pressures may be given in kilograms per square meter and 
the area F in square meters ; or the area may be given in square 
decimeters or square centimeters, and the pressures in kilograms 
on the same unit of area used in connection therewith. If the 
pressures are in millimeters of mercury, multiply by 13.5959; if 
in atmospheres, multiply by 10333. 



136 THERMODYNAMICS OF THE STEAM-ENGINE. 

Maximum Velocity of Flow. — According to the kinetic 
theory of gases, the pressure of a gas on the walls of the con- 
taining vessel is due to the impact of the molecules of the gas. 
To estimate the mean velocity of the molecules Joule* pro- 
ceeds in the following manner : The weight of one cubic meter 

of gas is — , and the pressure which it exerts on each of the six 

sides of a cubical vessel containing it is /. Suppose that the 

weight — of the gas to be divided into three equal portions, one 

of which oscillates between each pair of faces of the cube and 
produces the pressure by impact, first on one and then on the 
other of the pair. Now, if a body have a velocity equal to g, it 
will be brought to rest by a force equal to its weight acting on 
it for one second ; and that force acting for two seconds will 
bring it to rest and then impart to it the same velocity in the 
opposite direction. In two seconds there will be g impacts on 
each of the pair of faces, and it will be assumed that the effect 

of the impacts is equal to that of a pressure equal to — - kilo- 

grams on each face ; that is, on one square meter. The pres- 
sure will vary as the square of the velocity, since both the force 
required to reverse the velocity and the number of impacts in- 
crease with the velocity. Finally, Joule makes 

in which u is the mean velocity of the molecules of the gas. 
This may be written 



— -^ = Vgpv = VgRT . 

Fliegner assumes that the maximum velocity with which a 
gas can flow through an orifice is 

^,.a.. = ^JRT, = 16.9 1/7; 

when the French system of units is used. 

* Memoir Phil. Soc, vol. ix. p, 107. 



FLOW OF FLUIDS. 1 37 

P 

But if we make t^ = 0.5767 in equation (207), the velocity 
becomes, for French units, 

"^.na..^ I 7- 1 ^. 

Weisbach's Experiments on the Flow of Air. — Weis- 
bach ^ gives for the velocity of air through an orifice into the 
atmosphere 



w 
2^ 



= a.- [-(!)']: 



and by its use he finds for the coefficient of flow, from his own 
experiments, the results given in the following tables: 

FLOW OF AIR THROUGH AN ORIFICE. 
Diameter i centimeter. 

P 
Ratio of pressures— - 1.05 1.09 1.43 1.65 1.89 2.15 

P-i. 
Coefficient 0.555 0.589 0.692 0.724 0.754 0.788 

Diameter 2.14 centimeters. 

P 
Ratio of pressures— 1.05 1.09 1.36 1.67 2.01 

Coefficient 0.558 0.573 0.634 0.678 0.723 

FLOW OF AIR THROUGH A SHORT TUBE. 

Diameter i centimeter, length 3 centimeters. 

Pi 
Ratio of pressures — 1.05 i.io 1.30 

P-i 
Coefficient 0.730 0.771 0.830 

Diameter 1.4 14 centimeters, length 4.242 centimeters, 

P\ 
Ratio of pressures — ^ 1.41 1.69 

Pi 
Coefficient 0.813 0.822 

* Mechanics of Engineering, 



138 THERMODYNAMICS OF THE STEAM-ENGINE. 

Diameter i centimeter, length 1.6 centimeters, orifice rounded. 

P 
Ratio of pressures -r- 1.24 1.38 1.59 1.85 2.14 

Pi 
Coefficient 0-979 0.986 0.965 0.971 0.978 

Flow of Saturated Vapor. — For a mixture of a liquid and 
its vapor equation (140) gives 

so that equation (201) gives for the adiabatic flow from a re- 
ceptacle in which the initial velocity is zero, 

w^ I 

^ = ^ (^a - ^. + -^iPi - ^2P.) + /i^i - A^2 . . (211) 

Substituting for v^ and v^ from 

V =^ XU-\- (T, 



w* 



^ -- = ^1 - ^a + ^^f>^ - ^^P. + ^Pi^r^i - ^A^a^a + ^(^{Pi ^ A)' 

But 

p -f- Apu = r ; 



.•.^ — = ^a^--^.^ + ^i-^. + ^^(A-A)- • (212) 

The last term of the right-hand member is small, and fre- 
quently can be omitted. 

The value of x^ in the tube B, Fig. 29, at a distance from 
the orifice, can be determined by the equation 






FLOW OF FLUIDS. 1 39 

or, if the proper tables are lacking, we may use the approxi- 
mate form, 

7- — j^ \ ^^fee 7^ • 
-'a -^ 1 -^ 1 

It is necessary to remember that while the tables commonly 
give the pressure in pounds on the square inch, or in atmos- 
pheres, etc., /i and p^ in the last term of equation (212) are the 
specific pressures ; that is, the pressures in pounds on the square 
foot, or kilograms on the square meter. 

Substituting the first form for x^, equation (212) gives 

TJU^ X T 

^ 3^ = if (^-^»)+^»(^.-^^)+fe-?=)+^'^(A-A)- (213) 

Substituting the second form in equation (212), and neglect- 
ing the last term, we have the approximate formula 

lii^ X T T 

^2- =-7^(^I-^0+ ^2lOg,-^+^,-^,. . (214) 

The weight of fluid that will pass through an orifice having 
an area of F square meters or square feet may be calculated 
by the formula 

^ Fw 

G — p— . ...... (215) 

X^U^ + (T ^ ^^ 

The equations deduced are applicable to all possible mix- 
tures of liquid and vapor, including dry saturated steam and 
pure hot water. In the first place steam will be condensed in 
the tube, and in the second water will be evaporated. 

If steam blows out of an orifice into the air, or into a large 
receptacle, and comes to rest, the energy of motion will be 
turned into heat and will superheat the steam. Steam blow- 
ing into the air will be wet near the orifice, superheated at a 
little distance, and if the air is cool, will show as a cloud of 
mist, further from the orifice. 



I40 THERMODYNAMICS OF THE STEAM-ENGINE. 

Napier's Formulae for Flow of Steam. — As the result 
of a large number of experiments made on the flow of steam 
Mr. R. D. Napier concludes that the pressure in the throat of 
an orifice from which steam is flowing is never less than that 
pressure which, compared with the pressure in the reservoir, 
will give the maximum flow. 

The following approximate equations may be used with the 
English system of units : 

in which p^ is the pressure in the reservoir, and p^ is the pres- 
sure of the atmosphere, in pounds on the square inch, and G is 
the flow in pounds per second through an orifice having an area 
of F square inches. 

Rankine "^ concludes, from an examination of Napier's ex- 
periments and a comparison of them with formulae proposed 
by him, and a comparison of both with thermodynamic for- 
mulae, that the principle that the pressure in an orifice is never 
less than that which gives the maximum flow is well substan- 
tiated, and that the above equations may be used for rough 
calculations. 

Experiments on Flow of Steam. — The theory of the 
adiabatic flow of steam should apply to all mixtures of water 
and steam, including clear water, as from the water space of a 
boiler. Zeunerf points out an opportunity thus afforded of 
testing the equations, but states that experiments made by 
blowing water out of a locomotive boiler gave unsatisfactory 
results. 

Some experiments were made by Mr. B. G. Buttolph J in 
the laboratories of the Institute of Technology on the flow of 
steam through a brass tube 0.275 of an inch in internal diame-V 

^•' The Engineer, vol. xxvii. p. 359. 1869. 

f Mechanische Warmetheorie. 

% Proceedings Am. Mech. Eng. Soc. 1888. 



FLOW OF FLUIDS. 



141 



ter and eight inches long, and having the entrance orifice 
rounded to reduce cont^-action. The results are given in the 



following table : 



FLOW OF SATURATED STEAM. 



Num- 
ber 
of 
Experi- 
ment. 


Gauge Pressures. 

Pounds per square 

inch. 


Differ- 
ence of 
Pressures. 


Pressure of 
Atmosphere 
by Barome- 


Flow in 

Pounds 

per Hour. 


At En- 
trance. 


At Exit. 


ter. 
Pounds. 


I 


69.1 


4.4 


64.7 


14.7 


229.0 


2 


69.6 


9 


7 


59-9 


14 


7 


230.4 


3 


71-3 


14 


8 


56.6 


14 


7 


242.0 


4 


69.1 


19 


4 


49-7 




. 


232.0 


5 


71.0 


24 


4 


46.5 




. 


234-5 


6 


70.3 


29 


I 


41.2 




. 


229.0 


7 


72.0 


34 


2 


37.8 


14 


8 


232.0 


8 


72.0 


39 


5 


32.5 


14 


8 


221.4 


9 


71.6 


44 


2 


27.4 


14 


7 


216.5 



The following table gives the results of some experiments 
on the flow of steam through an orifice 0.25 of an inch in diam- 
eter, in a thin plate, made by Mr. G. P. Aborn "^ in the labora- 
tories of the Institute. 

FLOW OF STEAM THROUGH AN ORIFICE. 



Number of 


Higher 


Difference of 


Flow in Pounds 


Experiment. 


Pressure. 


Pressure. 


per Hour by Tank. 


I 


71.8 


0.92 


29.7 


2 


71 


5 


1.85 


43-1 


3 


71 


9 


2.79 


52.6 


4 


71 


6 


3.89 


67.6 


5 


71 


9 


5-55 


77.6 


6 


71 


8 


6.50 


84.2 


7 


71 


7 


8.07 


91.8 


8 


72 


9 


9-23 


93-9 


9 


72 


5 


12.8 


no. 3 


10 


73 


7 


15.9 


124.9 


II 


72 


7 


21. 1 


141.5 


12 


74 


2 


27.0 


156.8 


13 


71 


9 


33-7 


166.3 


14 


74 


3 


41.0 


180.7 


15 


72 


7 


49.2 


187.7 


16 


72 


9 


57-0 


195.8 


17 


73 


7 


04.4 


196.9 


18 


72 





68.4 


197.8 



* Thesis, 1886. 



142 THERMODYNAMICS OF THE STEAM-ENGINE^. 

Flow of Superheated Steam.— Equation (185) gives for 
the change of intrinsic energy 



' ' k-i 

so that for an adiabatic flow 

w"^ k 

which, by aid of equation (194), may be reduced to 

Equations (216) and (217) have the same form as the corre- 
sponding equations for a gas, since the expression for intrinsic 
energy has the same form for superheated steam as for a gas. 

Substituting for p^v^ from the characteristic equation. 



w 
2^ 



= ^{BT,-Cp4^i- (J)']. . . . (218) 



For calculation either equation (217) or (218) can be used, 
as may be convenient. 

EXAMPLES. 

1. Find the velocity of flow of air from the pressure of 6 
atmospheres in a reservoir to the pressure of 5 atmospheres in 
the throat of the orifice ; also, from 5 to 4 atmospheres, from 
4 to 3, and from 3 to 2, the initial temperature in each case 
being 30° C. 

2. Find the weight of air per second that will be discharged 
from an orifice i inch in diameter, from a reservoir having the 
temperature 60° F. and a pressure of 150 pounds per square 
inch, into the atmosphere. Calculate also with initial pressures 
100, 50, 30, and 20 pounds absolute. 

3. Find the weight of saturated steam per second, discharged 
through an orifice i inch in diameter, from a boiler having the 



FLOW OF FLUIDS. 1 43 

gauge pressure 60 pounds, into the atmosphere. Find also for 
the following values of x, 90, 80, 60, 50, 40, 20, and for hot 
water. Calculate also for initial pressures 80, 100, 1 50, 300. 
pounds by the gauge. 

4. Find the velocity of flow of superheated steam with the 
initial temperature 600° F. and initial pressure 30 pounds by 
the gauge, when the pressure in the throat of the orifice is 20 
pounds by the gauge. 

5. In Example 4 find the weight per second discharged 
through an orifice i inch in diameter. 



CHAPTER X. 

INJECTORS. 

An injector is an instrument by means of which a jet of 
steam acting on a stream of water with which it mingles, and 
by which it is condensed, can impart to the resultant jet of 
water a sufficient velocity to overcome a pressure that may be 
equal to or greater than the initial pressure of the steam. 
Thus, steam from a boiler may force feed-water into the same 
boiler, or into a boiler having a higher pressure. The mechani- 
cal energy of the jet of water is derived from the heat energy 
yielded by the condensation of the steam-jet. Similar instru- 
ments are used in which a jet of steam or air imparts motion 
to a stream of air, or a jet of water imparts motion to a stream 
of water, without a change of heat into mechanical energy. 

When the reservoir from which water is drawn is below 
the injector, the injector is called a lifting injector ; but when 
the reservoir is above the injector, so that water will flow in 
under the action of gravity, it is called a non-lifting injector. 



STEAM v^H 



10^ i T^F 

Fig. 30. 

Fig. 30 shows the section of the Mack lifting injector, and Fig. 
31 of the non-lifting injector, by the same maker. 

Method of Working". — To start the lifting injector, open 
the steam-valve a quarter or half of a turn, then open the valve 

144 



INJECTORS. 



145 



in the water supply ; as soon as water appears at the overflow 
open the steam-valve until it ceases to overflow. 

When the steam-valve is first opened a part of a turn the 
hollow spindle 5 is farther to the left and closes the orifice 6. 
A small stream of steam flows past 5, passes through the con- 
ical passage, and out at the overflow. The stream of steam 
flowing past 6 draws air with it from the chamber 5, and the 
partial vacuum thus produced draws water from the reservoir, 
which condenses the steam, and with it flows out at the over- 



'^'''i'g^^^^^^^:^^:^ 




flow in a continuous stream. When this stream is well estab- 
lished the steam-valve is opened wide, and a large jet flows past 
6, and is condensed in contact with the stream of water. The 
stream of water flowing through the conical passage has now 
sufficient velocity to leap across the opening at o and enter the 
conical passage 7, from whence it passes to the boiler. At the 
overflow is a valve, held open by a slender spring, which closes 
when the pressure at o is less than that of the atmosphere, so 
that air may not be forced into the boiler Avith the feed-water. 

It is customary to have a valve in the steam-pipe above the 
injector, which is closed when the injector is not working, and 
which is opened before starting the injector. It is necessary 
to have a check-valve in the boiler feed-pipe to prevent the 
water in the boiler from flowing back through the injector 
when the injector is not working. 

The action of the injector may be regulated, within limitS;^ 



146 THERMODYNAMICS OF THE STEAM-ENGINE. 

by manipulating the water- or steam-valve, or both. When the 
pressure of the steam is low or the lift small, it may be neces- 
sary to reduce the flow of water by partially closing the water- 
valve. 

To start the non-lifting injector the steam-valve is opened 
to clear the supply-pipe of condensed water, and then it is 
closed. The water-valve is opened till water appears at the 
overflow, upon which the steam-valve is opened till water 
ceases to run out at the overflow. 

It is apparent that the action and the construction of this 
form are simpler than those of the lifting injector. 

Theory of the Injector.— The efficiency of an injector 
and the proper proportion of its parts cannot be determined 
entirely from the known properties of steam, the more espe- 
cially as its action depends on the flow of steam. We shall 
first study its action under the assumptions that there is no 
loss from friction and radiation, and that we may use the equa- 
tions for the adiabatic flow of steam. It will also be assumed 
that the jet of steam at 6, Fig. 30, is immediately and com- 
pletely condensed by contact with the stream of water there. 

The quantities to be ascertained are : 

1. The velocity with which the steam issues from 6, Fig. 
30. This depends on the pressure and quality of the steam in 
the supply-pipe, and the pressure of the orifice 6. 

2. The quantity of feed-water that one pound of steam will 
force into the boiler. This depends on the temperature of the 
water in the reservoir, the temperatures of the water in the feed- 
pipe, and the pressure of the steam in the boiler from which 
steam is drawn and to which water is fed. 

3. The velocity with which the stream of water passes the 
narrowest orifice at 7 on the way to the boiler. 

4. The size of the steam and water orifices. 

Velocity of the Steam-jet. — Assuming that the flow of 
steam from the orifice 6 is adiabatic, equation (212) gives 



^6 



INJECTORS. 147 

in which p^ is the pressure of the steam in the supply-pipe, and 
p^ the pressure in the orifice 6. x^, r, , and q^ are the quahty of 
the steam, the heat of vaporization, and the heat of the liquid 
of the steam at the pressure /, ; and x^^ r,, and q^ are the cor- 
responding properties at the pressure p^. 
To determine x^ we have 

-^ 1 -^2 

Quantity of Feed-water per Pound of Steam. — The 

number of pounds of feed-water y delivered by one pound of 
steam may be found by assuming only that the losses from fric- 
tion and radiation may be neglected. 

The gain of heat by the feed-water in passing from the tem- 
perature 4 in the reservoir to the temperature /^ in the feed- 
pipe is 

^fc - ^3). 

The loss of heat in one pound of steam on condensation 
and reduction to the temperature t^ is 

The heat equivalent of the kinetic energy of the jet of water 
at its smallest section, where the velocity is F, which energy is 
expended in forcing the water into the boiler, is 

(1+7)-—' 
The assumption of no loss of heat gives 

y{^. - ^3) + (I + j) -^ = ^1^ + ^1 - ^4 . . (219) 

An approximate value of j/ can be obtained by neglecting 
the term containing V, so that 

x,r. A- a, — Q^ 



148 THERMODYNAMICS OF THE STEAM-ENGINE. 

An exact value of j/, in the general case, can be obtained 
by a series of approximations in combination with equation 
(222), the first approximation being obtained by aid of equa- 
tion (220). 

Velocity of the Water-jet. — Three cases may occur in 
different forms of injectors : 

1. The water in the supply-pipe may have a head vS, and 
the approaching water will have a momentum imparted to it 
by that head. 

2. The water in the supply-pipe may be lifted through a 
height vS, and a corresponding momentum must be imparted 
to it by the steam-jet. 

3. There may be neither lift nor head, and the approaching 
water will have no momentum. 

The first may be considered to be the general case, and may 
be made to include the other two by making the head nega- 
tive for one and zero for the other. 

The momentum oi \ -\- y pounds of water, at the smallest 
section of the water-jet, will be the sum of the momentum of 
one pound of moist steam in the steam-jet, plus the momentum 
imparted \.o \ -\- y pounds of feed-water by the head S. 

The momentum of i -|- j^ pounds of water in the water-jet is 

(1+7)^ 
g 

The momentum of one pound of steam is 

w 

g\ 

Let a be the area of the smallest section of the water-jet •; 
then the force exerted by the head of 5 water having the den- 
sity y on that area is 

Sya^ . 

This force acts on a mass 

Vya^ 



INJECTORS. 149 

of water per second, and imparts to it a velocity of 

^ Vya^ Sg 

feet per second, so that the momentum imparted to i -1- ^ 
pounds of water by the head 5 is 

Hence we have 



g g 



.••(i+.)iF-f) 



W, 



w 
'.V'-—r—V=Sg; . (221) 



•••^ = -^ + V'4(T^+*-- • (-^) 



W 

2(1+/) 



For the second case, in which the water is Hfted by the in- 
jectors through a height k, 



^ = -^V5TTS'-* ■ • <"'> 



w 

2(1+7) 



For the third case, in which the water enters the injector 
on the level of the jets, so that the momentum of one pound 
of steam in the steam-jet imparts the momentum which i -{- y 
pounds of water has in the water-jet, we have 

(i -\- y)V w 

w 

•••^ = 7+7' ^''^^ 

which maybe obtained from equation (221) by making 5 zero. 



150 THERMODYNAMICS OF THE STEAM-ENGINE. 

Sizes of the Orifices. — Since one pound of steam feeds jj/ 
pounds of water to the boiler, the steam required per second 
to feed G pounds of water will be 

G 

The specific volume of the moist steam in this orifice is as- 
sumed to be 

^2 = ^2^2 + ^» 

where x^ is determined by the equation for the adiabatic change 
from the pressure p^ in the boiler to the pressure p^ before the 
orifice. Consequently the area of the steam-orifice in square 
feet is 

^^^ g(^A + <r) 

yw 

The steam used by an injector is returned to the boiler with 
the feed-water, so that 

g(i+j) 

y 

pounds of water per second pass through the water-orifice. Its 
area in square feet should therefore be 

''-^~^fir ^^^^> 

The density y should properly be the weight of water per 
cubic foot, at the temperature in the feed-pipe, but the ordi- 
nary density 62.4 can be used instead. 

In all of the foregoing work the English units have been 
used, but the equations may be applied to problems stated in 
the French units, kilograms, and meters, without change. They 
may also be applied to other vapors that behave like steam. 

The diameters of the orifices of an injector are commonly 
given in millimeters or inches and fractions, while the areas by 



INJECTORS, 1 5 1 

the formulae are given in square feet or square meters. The 
reductions are readily made in every case. 

Problem. — Required the diameters of the orifices for an 
injector to deliver 1200 gallons of water per hour ; the tempera- 
ture of the feed-water being 180° F., and that of the water in 
the reservoir 100° F., while the pressure in the boiler is 45 
pounds. Assuming the steam supplied to the injector to be 
dry, and that the pressure in the steam-orifice is 0.6 of the ab- 
solute boiler pressure, we have for the determination of the 
quality of the steam in the steam-orifice 

wi^ g 9317 _^ 

753.2 ' ^ '^ 721.2 ' ' «^ ^' 

.-. X — 0.9683. 

The last term of equation (212) may here be neglected, so 
that 

— - = 909.5 - 902.1 -f 261.6 - 229.7 = 39.3 ; 



.-. ze; = 1/2 X 32.2 X 39-3 X 77^^ = 1403. 
The quantity of water delivered per pound of steam is 
909.5 + 261.6- 148.5 

y = — 148.5-68.0 = ^"•^^- 

The velocity of the water-jet is 

rr 1403 

y = = 102.4 ft. per sec. 

13.70 ^ ^ 

The injector is required to deliver 1200 gallons an hour, or 

1200 X 231 ^ , . , 

1728 X 60 X 60 = ^-^4456 cubic ft. per sec ; 

.*. G — 0.04456 X 62.4 — 2.781 pounds per sec. 



152 THERMODYNAMICS OF THE STEAM-ENGINE. 

The Specific volume of the moist steam in the steam-orifice 
is 

^2^2 + ^ — 0.9683 X 1 1.50 + 0.016 = 1 1. 1 5 cu. ft. 

The area of the steam-orifice is consequently 

2.781 X II. 15 ^^ 

a, — —^ — — 0.00174 sq. ft., 

12.7 X 1403 

and the diameter is 0.55 of an inch. 

By equation (226) the area of the water-orifice is 

2.781 X 13.7 . r^ 

a^ = ^ — — = 0.000469 sq. ft., 

62.4 X 12.7 X 102.4 ^ y H > 

and the diameter is 0.22 of an inch. 

Suppose that the injector was required to lift 20 feet, then 
the value of j/ is changed but Httle, and the values of w and ^^ 
not at all. The first approximation of Fwill be 



Y \2 X 13-7' 



V = --^^ + A / l:rT^^J + 20 X 32.2 = 108.3 



which gives for the diameter of the water-orifice 0.21 of an inch 
instead of 0.22, as found before. 

Limits to the Action of an Injector. — If the height of a 
water column equivalent to the pressure /, in the boiler, plus 
the height of the lift, be represented by h, then when 

h < — 

the water will enter the boiler with a residual velocity. If 

V 
^ = ^^ (227) 

the water will enter the boiler without residual velocity. This 
fixes the limit of the action of the injector, since it will fail to 
work if 

h> — . 



INJECTORS. 153 

Injectors are commonly tested by the makers under the 
conditions of service, with the pressure in the dehvery- or feed- 
pipe, 10 or 15 pounds above the pressure of the steam suppHed, 
to insure that the water-jet shall be able to overcome the boiler- 
pressure and the added resistance of valves and pipes. A re- 
sidual velocity is accompanied by a larger delivery by the in- 
jector and a higher temperature, and when the injector is used 
to feed a boiler is not accompanied by any loss of heat or en- 
ergy, radiation and friction being neglected. 

The height to which an injector will lift cold water depends 
on the form and proportions of the parts of the injector. In- 
jectors are seldom set to lift more than 20 feet. Since hot 
water gives off vapor at a pressure depending on its tempera- 
ture, it cannot be lifted to so great a height as cold water, 
either by an injector or a pump. 

The temperature of feed-water delivered by an injector is 
limited by the fact that the steam used must be condensed 
at the pressure existing in front of the steam-orifice. The 
temperature may be higher with a small hft than with a high 
lift, and may be increased if the water be supplied under 
pressure. 

The temperature of the water in the reservoir must be low 
enough to give the range of temperature required to condense 
the steam used. 

A pair of orifices for the steam- and water-jets of an injec- 
tor which give a considerable residual velocity with a range of 
temperatures well within the limits, will continue to work if the 
conditions be changed, but a limit is soon reached beyond which 
the injector will fail to act. Beyond the limit three cases may 
arise : (a) water will be wasted at the overflow ; {U) steam will 
appear at the overflow ; {c) air will be sucked in at the over- 
flow. In the last case the air drawn in may break the continu- 
ity of the water-jet. The other two cases, in addition to the 
waste of water or steam, are liable to interrupt the action of 
the injector. They are certain to do so if the overflow-valve is 
closed after the injector is started. 

Fixed Nozzle Injector. — The Mack injector shown by 



154 THERMODYNAMICS OF THE STEAM-ENGINE. 

Figs. 30 and 31 is of this type, that is, the water- and steam- 
orifices are both fixed. The action of the injector is controlled 
mainly by regulating the supply of steam at the steam-valve, 
though the supply of water may be reduced within limits at the 
water-valve. The overflow-valve allows water or steam to 
escape, but prevents air from entering. When the steam pres- 
sure is low or there is a head, it may be necessary to diminish 
the supply of water. 

An injector of this type has been known to feed water to a 
boiler with both water- and steam-valve open, and with steam 
escaping at the overflow. 

Giffard Injector. — This is the oldest form of injector in 
which the steam- and water-orifices were both adjustable. It 
had a hollow spindle, through which steam was first admitted 
to induce the flow of water, and this spindle moving inside a 
hollow cone regulated the supply of steam. The hollow cone 
was also movable, so that by it the water space surrounding it 
could be controlled. 

Automatic Injectors. — With either of the two preceding 
examples of injectors, the change of boiler-pressure is liable 
to require a regulation by hand, lacking which the inject- 
or may stop. In some forms the instrument is made auto- 
matic, as, for example, the Sellers injector shown by Figs. 32 
and 33. 

A is the receiving or steam tube, which is opened or closed 
by the valve X. Through it passes a hollow spindle, to the 
inside of which steam is admitted by the valve W, which can 
be opened without raising X from its seat, by moving the 
spindle until the shoulder just touches that valve. This small 
motion of the spindle admits steam for raising water till it 
overflows at P. When this occurs the spindle is drawn back 
and the steam-valve X opened wide, upon which the action 
should be complete and water should be forced into the boiler. 
The rod L is connected to the handle H in such a manner as 
to close the overflow when the steam-valve is wide open. To 
diminish the amount of water delivered by the injector the 
steam-valve may be partially closed. 



INJECTORS, 




Fig. 32. 




156 



THERMODYNAMICS OF THE STEAM-ENGINE. 



6TEAM 



The supply of water is controlled automatically by the 
movable piston iVTV, which moves freely in the cylindrical shell 

MMj and is guided also at 
the forward end ; as shown, 
it is as far forward as it can 
go. The impact of the wa- 
ter upon the piston tends to 
move it forward, and on the 
other hand water may pass 
through the orifice at O^ and 
produce a pressure tending to 
move the piston backward. 
Thus the supply of water is 
automatically adjusted to the 
steam. 

Double Injectors. — It 
was remarked that the tem- 
perature of the feed-water 
could be materially increased 
in an ordinary single injector 
by supplying the water un- 
der a head. The double in- 
jector consists of two parts, 
each essentially a single in- 
jector. The first part, called 
the lifter, draws water from 
the reservoir and forces it 
into a chamber, from which 
the second part, called the 
forcer, takes it and forces it 
to the boiler. The double 
injector also has the advantage that it is to a large extent self- 
regulating, since a rise of boiler-pressure which increases the 
flow of steam through the forcer-jet increases the flow of steam 
through the lifter-jet in like manner, and thus increases the 
supply of water, and also increases the pressure in the inter- 
mediate chamber. 




INJECTORS. 



157 



All double injectors are fixed-nozzle injectors and are lifting 
injectors. 

Fig. 34 shows the Hancock inspirator in section. The steam 
enters at B and flows to the lifter-jet directly beneath, and also 
supplies the forcer-jet at C, where there is a valve for control- 
ling the flow. The water enters at A and is delivered by the 
lifter to the intermediate chamber D, from which it is taken 
by the forcer and dehvered to the boiler. At i is a valve 
connecting the intermediate chamber with the delivery, and 
at 3 is the overflow-valve. 

To start the inspirator, close 2, and open i and 3. Let on 
steam, and when water appears at the overflow close i. Open 
2 a quarter of a turn, and then close the overflow, upon which 
the water will be forced to the boiler. No adjustment is 
necessary for varying steam-pressure, but the quantity and 
temperature of the water delivered may be varied by varying 
the steam- or water-supply. 




KiG. 35«. 



The Korting injector is shown by Figs, ^^a and 35<5. The 
arrangement and action of the parts is evident without detailed 



158 



THERMODYNAMICS OF THE STEAM-ENGINE. 



description. The handle is moved a short distance till the 
lower or forcer valve, which opens first, has given steam to the 
forcer, and water appears at the overflow. Then the handle is 




Fig. 3s3. 



pulled back as far as it will go. The overflow to the inter- 
mediate chamber closes when the forcer is started. 

The Hancock inspirator is also arranged to work by one 
continuous motion of a handle, when it is applied to loco- 
motives. 

Tests of Injectors. — The table opposite gives the results 
of experiments made on the Sellers self-adjusting injector hav- 
ing the combining tube or water-orifice 6 mm. in diameter at 
the smallest section. 

For each pressure of steam noted in column i, the water 
was delivered by the injector into the boiler under approx- 
imately the same pressure. The delivery was measured by 
observing the indications of a water-meter. The pressures in 
column 8 were obtained by throttling the steam supplied to the 
injector, and observing the pressure at which it ceased to work, 
each experiment being repeated several times with precisely 



INJECTORS. 



159 



EXPERIMENTS ON A SELLERS INJECTOR. 
(Diam. Water-orifice 6 mm.) 



upplied 
ressure 
r is de- 
j. Inch. 


Delivery 
in Cubic Feet per Hour. 


Temperature, 
Fahrenheit Degrees. 


1.1 
rt aj.2 

III 


11 


Pressure of Steam s 
to Injector, and 1 
against which Wate 
livered. Lbs. per S 


S 

D 

'I 


s 

'5 


2=^ 
il 

a « 

1^ 




Delivered Water. 


u 


a 
It 

< 


a 

It 

c > 

< 




I 


2 


3 


4 


5 


5 


7 


8 


9 


10 


75-3 


63.6 


0.845 


66 


100 


94 


3 


132 


20 


82.4 


61.2 


0.743 


66 


108 


104 


9 


134 


30 


94.2 


56.5 


0.600 


66 


114 


116 


16 


134 


40 


100. 1 


60.0 


0.599 


66 


120 


123 


22 


132 


50 


108.3 


64.7 


0-597 


66 


124 


125 


27 


131 


60 


116. 5 


63.6 


0.546 


66 


127 


133 


34 


130 


70 


124.8 


63.6 


0.510 


67 


130 


142 


40 


130 


80 


I33-0 


67.1 


0.505 


66 


134 


144 


46 


131 


90 


141-3 


69.5 


0.492 


67 


136 


148 


52 


132 


100 


147.2 


64.7 


0.456 


66 


140 


159 


58 


132 


TIG 


I53-0 


67.1 


0.439 


67 


144 


162 


63 


132 


120 


156.6 


73-0 


0.466 


67 


148 


162 


69 


134 


130 


161. 2 


74.2 


0.460 


66 


150 


165 


75 


130 


140 


166.0 


78.9 


0.476 


66 


153 


166 


81 


126 


150 


170.7 


70.6 


0.414 


66 


157 


167 


88 


121 



the same results. The temperatures in column 9 were obtained 
by gradually heating the water supplied to the injector, and 
noting the temperature at which it ceased to operate, each 
temperature recorded being checked by several repetitions of 
the experiment. 

Some experiments were made in the laboratory of the 
Institute of Technology, by Messrs. Bradlee and Blanchard,"^ 
on several styles of injector, of which the results are given in 
the following table : 



* Thesis. 1$ 



i6o 



THERMODYNAMICS OF THE STEAM-ENGINE. 



a 
■ \ 


•SuiraUcj 
luao'jsd £ 
pajB'inoiBO 


^ 

» 


vq 'J- >o 





N ro ON ; 


; NO ON N NO in 
; f^ 00 00 M M 


d 


q in 

ON W 


ro « 


•paiBjniBS 

inB3;s 
paiBinoi^o 


; 






• • • • N 


. • . On . 




: : 




•^uaiu 
-uadxg Ag 


m 


t-s fO 

O ro rn 


lO 


MD NO t^ lO ro 
r^' c^" (N n' ro 


vq 00 ro NO 
o' t^ ON 00 r^, M 





ro 00 

On w 


q ro 


•spunoj 
'jnoH J3d pasn uiBajg 


00 


?^ ^ 





!>. q !>. in N 

t^ ON 00 t>. ON 


in H CO lo M 

M H M 


s 


ON H 


NO CO 


•spunojj 

'jnoH 

aad p3J3A![3p jajB^w 


N 


lO t- t^ 

t^ ro 00 
H ro <N 




4 


H q c) Tj- 

H On H c^ 
^ in 00 S t^ 


CO t-. ro ro n 
t^ NO 00 rl r? K? 


NO 

o' 




i i 










•spunojj 
J3d pajiddns x^vsj^ 


^ 
N 


Tf ^ 




§ 


^ O in On 00 

f § 1 |n| 


ro NO ro in in 

H ■* H NO NO 00 
^ ^^ S 2" ? 


d^ 


ro vq 
in t-~ 

00 o^ 


M NO 
H C.^ 

00 00 




•.iij3Aipa 


00 





00 


^ NO t> 

T^ P) ro On in 
ro ro ^ >*- O 


m (N 00 ro H t^ 

8^ a nS^ i i i 


NO 


in 

Ng^ ^ 

M (-1 


tJ- d< 


•3;b!P9uij35ui 


K 


s K ^ 


4- 


VO t^ 00 t~~ C^ 

p. Ng ?:s N^ 






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-"l- 

00 00 


^ '.'■':'• l 










•Xlddng 


?> 


^ ^ S) 


■^ 


ro On On 00 in 

00 vd NO c^ 'i- 
T*- Ti- m NO in 


N 00 H ON -sj- 

in d NO 00 i-i H 
in NO in in NO NO 





CO On 


H 00 


•XJn^J^p^J 
JO saqoui ui uopons 


00 

4 


-* o> 1^ 
4 lA ^d 


q 

ON 


o> in in On NO 
00 t>. t>. c^ 4 


tx . ■ On 00 On 

ro • • in Tt- Nd 


ON 


H 00 


N NO 


•J93jl UI ijn 


^ 


l-~ VO 





H in in ON (s 
oo 00 00 in 


P) On in t^ ^ oo 

^ t>. Tt- Nd ui t^ 





ON ON 


t^ ro 


•qouj -bg J3d spunO(j 
'jaiaraoaBg 




4^^ °4- 


t^ 


t^ t^ NO ON 


00 00 00 t^ 00 

in TC .^ Tt- Tt- Tf 


ON 


q 00 


00 t>. 

4 4 


■ A 
W c 
D . 

a CO 

il 
-I 


•AjSAipQ 


1 


c^ r^ t~ 


lO 


H ro in ro H 
t^ C-- t-^ t^ 


(N N T^ ^ m ro 


t-^ 


t^ t-« 


in N 


•3JBip3aiJ35UI 


i - 


ro in 00 

cj H O 


00 




i«- in NO ^ 

M H ri- 








ON 


^ : : : : : 




■ S 


•jaiiog 


q 
P) 


ro m q 

fi ?!, P. 


P. 


No in in H t^ 

NO NO P. NO N 


N ro M 00 ro 00 

N p. tt tt t.. NO 


ro 


in -"J- 


-f 


•ao^Dsfui JO aoi-B^ 


8 

aj 


. z i: 


;: 




' i ' ' '■ '■ 


- 




- - 


uaquinjsi 


" 


N ro ■>*■ 


m 


NO t^ 00 ON 


M ei ro Tt- m NO 


(.^ 


00 ^ 


8 S 











INJECTORS. l6l 

Sizes of Orifices. 

Hancock: lifter, steam, 0.I14 

'' forcer, steam, 0.206 

" " water, ...... 0.149 

Lombard : steam, 0.224 

" water, 0.164 • 

Dodge: steam, 0.161 

" water, 0.131 

The experiments 15 to 21, inclusive, were made with im- 
proved methods of reducing the evaporation of the hot water 
delivered by the injector, and the results are more consistent 
and reliable than the preceding ones. It is apparent that the 
weight of steam used, which is obtained by taking the differ- 
ence between the weights of water supplied and delivered, is 
diminished by the evaporation, and that consequently the 
experimental quantity of water delivered by one pound of 
steam is made too large thereby: this explains part of the dis- 
crepancy of the first fourteen experiments. 

The calculations for Experiment 17 on the Dodge injector, 
on the assumption that the pressure in the steam-orifice is 0.6 
of the absolute boiler-pressure, are as follows : 

Pressure in the steam-orifice, 

0.6 X 86.2 = 51.7 pounds. 

Quality of steam in the steam-orifice on the assumption of 
0.03 priming, 

0.97 X 891.8 , 9i6;ir, 

-^j;rv — + 04592 = + 0.4138 ; 

777-7 ^^ 7A2>'7 ^ 

x^ = 0.94. 
Velocity of the steam in the steam-orifice, 

^^"6^ =8^5 -86, +287.3 -253.3; 
,-. w — 1398 feet per second. 



1 62 THERMODYNAMICS OF THE STEAM-ENGINE. 

Specific volume of steam in steam-orifice, 

v^ = 0.94 X 8.239 + 0.016 = y.y6. 

Flow of steam in pounds per second, 

7r(o.i6i)=^ X 1398 

— ^ ;; ^ = 0.2547 pounds ; 

4 X 144 X y.'/6 ^^' ^ ' 

Napier's rule gives 0.2509 pounds. 

The flow of steam per hour is 91.7 pounds by the calcula- 
tion, instead of 93.1 by experiment. 
The velocity of the water-jet is 

1398 

V = ,— =: 126 feet per second. 

lO.I + I ^ 

The head equivalent to 74 pounds per square inch is 

74 X 144 

/jT_ — 22: ~ 1^70.7 feet. 
62.4 ^ ^ 

Adding, in the lift, 10.4 feet, gives 181.1 feet. The velocity 
required to overcome this head is 



1/2 X 32.2 X 181. 1 = 108 feet per second. 

If it be assumed that the jet in the water-orifice is entirely 
water, then the velocity calculated from the weight of water 
delivered per hour and the diameter of the water-orifice is 

1032.6 ^(-131)' 

= 78 feet per second. 



3600 X 62.4 ' 4 X 144 

From these calculations it appears that either the steam is 
not entirely condensed till after the smallest section of the water- 
orifice is passed, or else there is a ve7ia contracta. A similar 
result was found by the makers of the Sellers injector for some 
of the experim.ents on page 159. 

Exhaust-steam Injectors. — It has been pointed out that 
an injector may be made to deliver water against a pressure 
higher than the pressure of the steam supplied. An extreme 



INJECTORS. 163 

example of this is found in injectors which use the exhaust 
steam of a non-condensing engine for feeding a boiler. Such 
an injector must be supplied with cold water : it cannot deliver 
water at a high temperature, and it carries with it some of the 
oil from the engine cylinder. 

The Injector as a Pump. — The injector is commonly used 
as a boiler-feeder, in which office it may be advantageous as a 
feed-water heater, since all the heat not expended as work in 
forcing the water into the boiler is returned to the boiler with, 
the water, though at a lower temperature. When used as a 
pump, to deliver water against a head, the heat given to the 
water is often thrown away, and may be prejudicial ; for such 
work the injector has a very low efficiency. 

Acids and solutions are sometimes raised by injectors of 
special construction made to resist the action of the fluids. 

Let the height of one reservoir above the other, through 
which the water is to be raised, be H \ then 

H ^h^s, 

in which h is the head above the injector and s is the distance 
the water is lifted. It is desirable that there shall be little or 
no residual velocity ; hence by equation (227) 

Equation (221) for this case becomes 

w 

or, substituting for V from the equation above, and reducing 

w \'2s^h w Vh , ^^ 

i-\-y= J , = 7 -. . ^ (228) 

2gh+gs ./-.(;, + iJ ^ 



2gy 



An inspection of equation (228) shows that the quantity of 
water raised per pound of steam increases with w, which de- 
pends on the steam-pressure and the quality of the steam, but 
is independent of the pressure in front of the orifice, when the 



164 FHER MOD YNA Mies OF THE STEAM-ENGINE. 

steam-pressure is more than fifteen pounds by the gauge. The 
quantity of water raised per pound of steam decreases with the 
lift k^ and the suction s. The greatest practical lift is about 
26 feet. 

Problem. — Required the number of pounds of water raised 
per pound of steam, through a total height of 100 feet, the 
injector being 20 feet above the lower reservoir, and the steam 
pressure being 45 pounds by the gauge. 

The velocity of the steam w is 1403 feet per second ; con- 
sequently by equation (228) 

1403 VYo 
I +y = — ^^7^ : = 17.4; 



/ 



2<^ 



(»»+?) 



,\ f = 16.4. 

If the total height were 50 feet, then the number of pounds 
of water per pound of steam would be 22.9. 
In the first case the work done is 

16.4 X 100 = 1640 foot-pounds, 

and in the second 

22.9 X 50 = 2290 foot-pounds. 

It consequently appears that it is more economical to raise 
water through large than through small heights by this method. 

The following calculation shows that the consumption of 
steam by an injector used as a pump is extravagant when 
compared with a pumping engine. Let the injector be sup- 
posed to use one pound of steam per second ; in the first case 

1640 
its horse-power is , and the consumption of steam per 

horse-power per hour is 

550 X 60 X 60 



1640 



= 1200 pounds. 



INJECTORS. 



165 



In the second case the consumption is 1700 pounds per 
horse-power per hour. 

When the injector is used as a boiler-feeder its action is 
first that of a pump, — in which its efficiency, as has been seen, is 
small, — and second, that of a feed-water heater ; and its second 
action is useful to such a degree as an independent feed-water 
heater using boiler steam would be. Feed-water may some- 
times be heated by exhaust steam or by hot gases beyond the 
boiler, in which case heat that would otherwise be wasted is 
made useful. It is to be remarked that a much greater gain 
would result from the substitution of a condensing engine, in 
the first instance, were it possible to do so ; and that, in the 
second instance, it is difficult to properly heat feed-water with 
the gases that leave an economical boiler. 

Water -injector. — Fig. 36 represents a device called a 
water-injector, in which a small stream of water in the pipe M 




Fig. 36. 

flowing from the reservoir R raises water from the reservoir R" 
to the reservoir R' . 

Let one pound of water from the reservoir i? draw j pounds 
from R" ^ and deliver i -\r y pounds to R' , Let the velocity of 
the water issuing from A he v; that of the water entering from 
R" be v^ at N; and that of the water in the pipe O he v^. 
The equality of momenta gives 

V+^V,=:{l+y)v, (229) 



1 66 THERMODYNAMICS OF THE STEAM-ENGINE, 

Let X be the excess of pressure at M above that at N ex- 
pressed in feet of water ; then 

v^ = 2gx ; 

V^ =2g{H-\-x)) 
v: =z 2gijl + X\ 

Substituting in equation (229), 



^rH-\-x-\-y^x^{\-^y)^h-\-x\ 



S/H-\-x - V'h-^x 

■■■y= v^k^.-v-. (^30) 

It is evident from inspection of the equation (230) that y 
may be increased by increasing x ; for example, by placing the 
injector above the level of the reservoir so that there may be 
a vacuum in front of the orifice A. 

If the weight G of water is to be lifted per second, then 

— pounds per second must pass the orifice A, G pounds the 

space at N^ and (i A- y)G pounds through the section at O -, 
which, with the several velocities v, v^ , and v^ , give the data 
for the calculation of the required areas. 

Problem. — Require'd the calculation for a water-injector to 
raise 1200 gallons of water an hour, H = g6 ft., ^ == 12 ft., 
;ir = 4 ft. 

Vx—V^ = 2; VJlX ^= Vwo= 10; VA-\-x= V16 = 4- 

10 — 4 

4 — 2 

The velocities are 



V = V2 X 32.2 X 100 = 80.25 feet per second; 
v, = V2X 32.2 X 16 = 32.10 feet per second; 
v^ = V2 X 32.2 X 4 = 16.05 feet per second. 

1200 gallons an hour = 0.04452 cubic feet per second. 



INJECTORS. 167 

The areas are 

0.04452 
a = 7^ = 0.000185 square feet; 

3 X 80.25 ^ ^ 

4 X 0.04452 ^ ^ , ^ 
^ /N ^D __ Q o5ig^ square feet ; 



3 X 32.10 
0.04452 



0.00277 square feet. 




'~ 16.05 

The diameters corresponding to the velocities v and v^ are 

d = 0.18 of an inch ; 
</^ = 0.58 of an inch. 

The area a^ is of annular form, having the area 0.4 of a 
square inch. 

Ejector. — The investigation of the injector used as a pump 
showed it to be a very wasteful machine, especially when the 
water was lifted through a small 
height. The efficiency is much 
improved by arranging the instru- 
ment as in Fig. 37, so that the 
steam nozzle A shall deliver a 

small stream of water at a high velocity, which, as in the water- 
injector, delivers a larger stream at a less velocity. Each addi- 
tional conical nozzle increases the quantity at the expense of 
the velocity, so that a large quantity of water may be lifted a 
small height. 

Ejectors are commonly fitted in steamships as auxiliar}^ 
pumps in case of leakage, a service for which they are well 
fitted, since they are compact, cheap, and powerful, and are 
used only in emergency, when economy is of small conse- 
quence. 

Ejector-condensers. — When there is a good supply of 
cold condensing water, an exhaust-steam injector, using all the 
steam from the engine, may be arranged to take the place of 
the air-pump of a jet-condensing engine. The energy of the 
exhaust steam flowing from the cylinder of the engine to the 



1 68 THERMODYNAMICS OF THE STEAM-ENGINE. 

combining tube, where the absolute pressure is less and where 
the steam is condensed, is sufficient to eject the water and the 
air mingled with it against the pressure of the atmosphere, and 
thus to maintain the vacuum. 

Problem. — Suppose that the absolute pressure in the cylin- 
der of an engine is 4 pounds absolute, and the pressure in 
the steam-orifice of an ejector-condenser is 2 pounds absolute : 
find the pounds of condensing water per pound of steam and 
the velocity of the water-jet. Let the exhaust steam contain 
ten per cent of moisture, then the velocity of the steam-jet is 
obtained from 

Aw" 0.9 X 1007.2, X- N , o / 

"^ "" 613.8 (^53-09 - 126.3) + 587(0.2203 - 0.1754) 

+ 12 1.4 — 94.4 = 69.2 ; 

.'. w = 1300 feet per second, nearly ; 



_ o.9 X 1007.2 -[- 12 1.4 — 94.4 _ 
68.01 — 28.12 



y = — — ^o\. ^o " — ^^ = 22i 



j;300_^ 

22-^ I ^ 

The velocity required to overcome the pressure of 12.7 
pounds per square inch is 43 feet per second. 



EXAMPLES. 

1. In the problem given on page 151 suppose that the 
steam contains 10 per cent of moisture and make all the re- 
quired calculations. 

2. In the same problem let the lift be 10 feet and make all 
calculations, the steam having 5 per cent of moisture. 

3. An injector which feeds a boiler having a pressure of 6 
atmospheres takes feed-water at 20° C, and delivers it at 80° 
C. How many kilograms of steam are fed by one kilogram of 
water? 



INJECTORS. 169 

4. An injector which feeds a boiler having a pressure of 100 
pounds by the gauge deHvers 16 pounds of water for each 
pound of steam : the initial temperature of the feed-water is 40° 
C; what is the final temperature ? No lift nor head. 

5. Suppose an injector is used to supply an ether vaporizer 
in which the temperature* is 100° C, how many kilograms of 
liquid will be delivered per kilogram of dry vapor, when the 
initial and final temperatures of the liquid fed are 10° C. and 
50° C. ? 

6. Suppose that an injector supplied with dry steam at 3 
atmospheres is used to pump chloroform against a head of 30 
metres of the liquid. How many kilograms of liquid will be 
delivered by one kilogram of steam if the initial and final tem- 
peratures of the liquid are 0° and 20° C. ? 

7. An exhaust steam-injector is supplied with steam at 
atmospheric pressure. How many pounds of water per pound 
of steam will it deliver to a boiler at a pressure of 60 pounds by 
the gauge, the initial and final temperatures of the feed-water 
being 40^ and 80° F. ? 

8. An injector is used to pump water against a head of 100 
feet, it is set 20 feet above the cistern, and is supplied with dry 
steam at 80 pounds gauge pressure. How many pounds of 
water will be raised per pound of steam ? What is the con- 
sumption of steam per horse-power per hour? If the initial 
temperature of the feed-water is 60° F., what will the final 
temperature be? What is the efficiency of the instrument as 
a heat-engine ? 



CHAPTER XL 

HOT-AIR ENGINES. 

Engines of Maximum Efficiency. — In order to have the 
maximum efificiency, an engine must work on such a cycle that 
its working substance shall always have the temperature of the 
source of heat when acquiring heat, and the temperature of 
the refrigerator when rejecting heat ; that is, the engine must 
be reversible. 

The older forms of hot-air engines all had the source of 
heat at one constant temperature and the refrigerator at an- 
other lower constant temperature. To have the maximum 
efficiency it was required that the working substance should 
receive heat from external sources at one temperature, and 
reject heat to external sources at one temperature only. 

Carnot's engine is the only simple engine which can fulfil 
these conditions when air is the working substance. The cycle 
of that engine has never been adopted in practice, since it 
involves incompatible requirements ; that is, the isothermal 
changes should be very slow and the adiabatic changes should 
be very rapid, to make the cycle of an actual engine approxi- 
mate to the ideal cycle. 

By aid of a device called a regenerator or economizer, actual 
engines have been made which have an ideal cycle of maximum 
efficiency. Such a cycle is represented by 
Fig. 38. The curves DC a.nd AB are isother- 
mals, which form those parts of the cycle dur- 
ing which heat is received from the source 
and rejected to the refrigerator. The curves 
BC and DA correspond to the adiabatic lines 
- of Carnot's cycle, and must fulfil the one con- 




^^' ^ ■ dition, that the heat given to the regenerator 

during one operation, as that represented by BC, must be equal 

170 



HOT-AIR ENGINES, I/I 

to the heat received from the regenerator during the converse 
operation DA, 

The relation between the curves BC and DA may be de- 
termined as follows : Let the equations to BC and AD be 

then by aid of the characteristic equation of the working sub- 
stance, 

/(/, V, t) = o, 

V may be eliminated, giving 

p=<p(T), p' = 'i>{T), 

for the equations of the curves. 

Draw the intermediate isothermals XZ and H^Fwith a dif- 
ference of temperature dt ; then the heat received by one unit 
of weight of the substance in passing from W to X \s 

dQ = Cpdt -\- mdp^ (230) 

and that rejected from Zto Fis 

dQ = Cpdt-\-m'dp' (231) 

The conditions of the problem will be fulfilled by making 
equation (230) equal to equation (231), so that 

mdp = m'dp' , 
Substituting for m from equation (53) gives 

(5),*=(f)//- 

Deducing the values of the partial differential coefficients 



172 



THERMODYNAMICS OF THE STEAM-ENGINE. 



from the characteristic equation for a gas, and substituting, we 
have 



dp__dp' 

P ~7' 

'.p^Cp'. 



(232) 



That is, the required relation is that the ratio of the pressures 
at the points cut by any isothermal from the paths DA and 
BC must be constant. 

Stirling's Engine. — This engine was invented in 1816, and 
was used with good economy for a few years, and then rejected 
because the heaters, which took the place of the boiler of a 
steam-engine, burned out rapidly. It is described and its per- 
formance given in detail by Rankine in his Steajn-engine. An 
ideal sketch is given by Fig. 39. ^ is a dis- 
placer piston filled with non-conducting ma- 
terial, and working freely in an. inner cylin- 
der. Between this cylinder and an outer one 
from A to C IS placed a regenerator made 
of plates of metal, wire screens, or other ma- 
terial, so arranged that it will readily take, 
heat from or yield heat to air passing through 
it. At the lower end both cylinders have a 
hemispherical head ; that of the outer cylin- 
der is exposed to the fire of the furnace, and 
that of the inner is pierced with holes through which the air 
streams when displaced by the plunger. At the upper end 
there is a coil of pipe through which cold water flows. The 
working cylinder H has free communication with the upper 
end of the displacer cylinder, and consequently it can be oiled ^^ 
and the piston may be packed in the usual manner, since only " 
cool air enters it. 

In the actual engine the cylinder H is double-acting, and 




Fig. 39. 



p 


A 


y 






X 


\ 




W 


Xn^ 






^^ 


z 




D 




Y 






C 





V 



HOT-AIR ENGINES. 1 73 

there are two displacer cylinders, one for each end of the work- 
ing cylinder. 

If we neglect the action of the air in the clearance of the 
cylinder //and the communicating pipe, we have the following 
ideal cycle. Suppose the working piston to be at the begin- 
ning of the forward stroke, and the displacer 
piston at the bottom of its cylinder, so that we 
may assume that the air is all in the upper 
part of that cylinder or in the refrigerator, 
and at the lowest temperature T^ , the condi- 
tion of one pound of air being represented 
by the point D of Fig. 40. The displacer 

1 1-111 Y\G. 40. 

piston is then moved quickly by a cam to 
the upper end of the stroke ; while the working piston moves 
so little that it may be considered to be at rest. The air is 
thus all driven from the upper end of the displacer cylinder 
through the regenerator, from which it takes up heat aban- 
doned during the preceding return stroke, thereby acquiring 
the temperature T^ , and enters the lower end of that cylinder. 
During this process, the line AD of constant volume is de- 
scribed on Fig. 40. When this process is complete, the work- 
ing cylinder makes the forward stroke, and the air expands at 
constant temperature, this part of the cycle being represented 
by the isothermal AB of Fig. 40. At the end of the forward 
stroke the displacer piston is quickly moved down, thereby 
driving the air through the regenerator, during which process 
heat is given up by the air, into the upper part of the displacer 
cylinder ; this is accompanied by a cooling at constant volume, 
represented by the line BC. The working piston then makes 
the return stroke, compressing the air at constant temperature, 
as represented by the isothermal line CD, and completing the 
cycle. 

To construct the diagram drawn by an indicator, we may 
assume that in the clearance of the cylinder H, the communi- 
cating pipe, and refrigerator there is a volume of air which 
flows back and forth and changes pressure, but remains at the 
temperature T^ . If we choose, we may also make allowance for 



174 



THERMODYNAMICS OF THE STEAM-ENGINE. 



a similar volume which remains in the waste spaces at the 
lower end of the displacer cylinder, at a constant tempera- 
ture Z'jo 

In Fig. 41, let ABCD represent the cycle of operations, 
without any allowance for clearance or waste spaces; the 
minimum volume will be that displaced by the displacer pis- 
ton, while the maximum volume is 
larger by the volume displaced by the 
working piston. Let the point E 
represent the maximum pressure, the 
same as that at A ; and the united 
volumes of the clearance at one end 
of the working cylinder, of the com- 
municating pipe, of the clearance at 
the. top and bottom of the displacer cylinder, and the volume 
in the refrigerator and regenerator. Each part of this com- 
bined volume will have a constant temperature, so that the 
volume at different pressures will be represented by the hyper- 
bola EF. To find the actual diagram A' B' C D\ draw any 
horizontal line, as sy, cutting the true diagram at u and v^ and 
the hyperbola EF at t ; make ux and vy equal to st ; then x 
and y are points of the actual diagram. The indicator will 
draw an oval similar to A'B'C'U with the corners rounded. 

To show that the diagram. Fig. 40, fulfils the condition for 
maximum efficiency, draw an intermediate isothermal XY, 
Since DA and BC are lines of constant volume, 




Fig. 41 









5 — A. 



.-•A 



A — Qy 



The diagram in Fig. 42 was reduced from an indicator-card 
from a recent hot-air engine made on the same principle as 
Stirling's hot-air engine. To avoid destruction of the lubricant 
in the working cylinder Stirling found it advisable to connect 
only the cool end of the displacer cylinder with the work- 



HOT-AIR ENGINES. 1/5 

ing cylinder, and had two displacer cylinders for one working 
cylinder. It has been found that a good mineral oil can be 
used to lubricate the displacer pis- 
ton of the new engine, and that 
the hot end also of the displacer 
piston can be advantageously con- 
nected with the working cylinders, 

of which there are two. Thus each ^'^- '^^• 

working cylinder is connected with the hot end of one dis- 
placer cylinder and with the cool end of the other displacer 
cylinder. 

The distortion of the diagram Fig. 42 is due in part to the 
large clearance and waste space, and partly to the fact that the 
displacer pistons are moved by a crank at about 70° with the 
working crank. 

Ericsson's Engine. — This engine consists essentially of a 
working cylinder, a compressing pump, and a reservoir. To 
give a perfect ideal cycle, a regenerator and a refrigerator are 
required. The pump, which must have a water-jacket which 
acts as a refrigerator, draws air from the atmosphere at con- 
stant pressure, compresses it at constant 
temperature, and forces it into the reser- 
voir under constant pressure. The pump 
cycle is represented by the diagram EDAF 
(Fig. 43). The engine draws air from the 
reservoir through the regenerator, during 
which process it is heated from the tern- ^'^- ^^3- 

perature T^ to T^ ; the supply is then cut off by a slide-valve, 
and the air in the cylinder expands at constant temperature 
down to the atmospheric pressure. On the return stroke the 
air is forced from the cylinder at constant pressure through the 
regenerator, being thereby cooled to the temperature T^. The 
engine cycle is represented by the diagram FBCE. The dia- 
gram of effective work is ABCD, which fulfils the condition of 
maximum efficiency, since AD and BC are isothermals, and 
AB and CD are lines of constant pressure. 

The actual engine does not expand down to the atmospheric 



p 

F A 


B 


Vg 




\ 


\ 


-.c. 


E D 





H 


v' 



1/6 THERMODYNAMICS OF THE STEAM-ENGINE. 

pressure, so that the diagram is cut short by a Hne Hke GH, 
Also, the clearances of the two cylinders introduce irregularities 
and modifications of the diagram. 

Gas-engines. — The various forms of gas-engines in common 
use are hot-air engines, in which the air is heated by the com- 
bustion of gaseous fuel mixed with the air. At full power 
there is one working stroke for two revolutions, the engines 
being single-acting. Fig. 44 gives the cycle 
commonly employed. At the end of the 
working stroke the pressure suddenly falls 
to that of the atmosphere, and on the re- 
turn stroke the gases in the cylinder are ex- 
pelled at atmospheric pressure. On the for- 
ward stroke the new charge of an explosive 




Fig. 44. mixture of gas and air is introduced, and on 

the return stroke the charge is compressed. These three opera- 
tions are represented by CE^ EC, and CD. At the end of the 
compression stroke the charge is ignited, and the air and gases 
are heated at constant volume by a very rapid combustion or 
explosion. During the forward stroke the gases resulting from 
the explosion expand, doing work. The two operations com- 
pleting the cycle are represented hy DA, AB. The cylinder is 
kept cool by circulation of water to prevent its destruction by 
the intense heat of the explosion. This cooling influences both 
expansion and compression curves ; also the expansion curve is 
modified by the fact that the explosion is not instantaneous, 
but continues throughout nearly the whole of the forward 
stroke. 

The efficiency of this cycle, on the assumption of instanta- 
neous explosion and adiabatic expansion and compression, is 
easily found. For the works of expansion and compression we 
have 



" K-l 
* K-l 






HOT-AIR ENGINES. lyj 

T 

But V, = Va, Vi,=: V,, pa = ^ Pdy 

■L d 

and the heat given to the gases by explosion, if c^ is the mean 
specific heat of the mixture at constant volume, is 

Q = clT^-T,); 






^ = I - l-;j (233) 

The remarkable conclusion from this last equation is that 
the efficiency for such a cycle does not depend on the differ- 
ence of temperatures, but rather on the degree of expansion and 
compression. 

Note. — For a full discussion of the theory and practice of gas-engines refer 
to D. Clerk's Gas-engines. 



CHAPTER XII. 



THE STEAM-ENGINE. 



Carnot's Cycle. — In the steam-engine the source of heat 
is ultimately the fire of the furnace, but the heat received by the 
engine is communicated at the temperature due to the steam- 
pressure in the boiler. In like manner the lower temperature 
is that due to the pressure of the vapor in the condenser, or, if 
none is used, it is the temperature of boiHng-point under at- 
mospheric pressure. Consequently heat is received and reject- 
ed at constant temperature ; and as a regenerator cannot be 
used, the only cycle of perfect efficiency is Carnot's cycle. The 
advantage to be derived from the discussion of this cycle is that 
from it the maximum performance of steam-engines may be 
calculated from laboratory experiments only, 
which experiments are susceptible of a de- 
gree of refinement impossible with engine ex- 
periments. The efficiency of actual engines 
is always inferior to that of Carnot's cycle, 
because the cycle of such an engine is incom- 
plete and non-reversible, and there are un- 
avoidable losses from friction, leakage, and 
loss of heat. 

Let Fig. 45 represent the cylinder of Car- 
not's engine, using M pounds of a mixture of steam and water, 
together with the cycle of operations. Beginning at the point 
a, the cycle is as follows : 

(i) Expansion at constant temperature and pressure, repre- 
sented by ab, during which some of the water is vaporized, and 
the heat absorbed is 



V 









Fig. 45. 



e, = Mrlx, - x:). 



(234) 



STEAM-ENGINE. 1 79 

(2) Expansion without communication of heat, represented 
by the adiabatic be, till the temperature is reduced from T^ to 
Tjj . This expansion is accompanied by a condensation of steam, 
so that Xi, becomes x^, which may be calculated by the equa- 
tion 



r^r . „ r^x^ 



1" c 



7^ 1 ^. - 7^ +<^x (235) 

J. ^ -* 1 

(3) Compression at constant temperature and pressure, repre- 
sented by cd, during which steam is condensed and heat is re- 
jected to the-amount 

Q,^Mrlx,-x^ (236) 

(4) Compression without communication of heat, represent- 
ed by da, till the temperature is raised from T^ to T^ and the 
cycle is completed. For this operation we have 



"^^d. = -^+^ (237) 

Equations (235) and (237) give 

^c-^d = -r-^{^b-x^\ (238) 

.\Q, = M^rix,-x:) (239) 

The efficiency is therefore 

AW Q,-Q, T,-T, 

and the effective work is 

'^ ~ A T, ~ A T, ■ ■ ■ ^^ ' 



i8o 



THERMODYNAMICS OF THE STEAM-ENGINE. 



It is convenient for calculation to assume that at the begin- 
ning of the expansion represented by ab the mixture is all 
water, and that at the end it is all steam, so that x^ =. o and 
Xi, = I. This assumption gives 

Mr T — T 
W^--^^^^-^^; (242) 



'.M = 



A 
AW 



T. 



T. 



T — T 



(243) 



To find the water evaporated per horse-power per hour in 
such an engine, make IV equal to 60 X 33,ooo foot-pounds,. 

and substitute for A its value, - — - , which gives the expression 



778 



60 X 33000 



= 2545 



T, 



T^ 



(244) 



778 r^T.-r:) '^'riT, 

The following table was calculated by aid of equations (240) 
and (241). The lower temperature for non-condensing engines 
is that of boiling-point of water under atmospheric pressure ; 
for condensing engines it depends on the perfection of the 
vacuum maintained in the condenser, which was assumed in 
these calculations to be 1.5 pounds of absolute pressure. It 
should be remarked that the ratio of the steam consumption of 
two cycles, actual or ideal, is not necessarily the ratio of the 
efficiencies. 

EFFICIENCY AND CONSUMPTION OF A PERFECT STEAM- 
ENGINE. 



Initial Pressure 

by the Gausre, 

above the 

Atmosphere. 



15 
30 
60 
100 
150 
200 
300 



Condensing Engines. 



Efficiency 



0.l8q 
0.215 
0.249 
0.278 
0.302 
0.320 
0.347 



Pounds of Steam 
per H. P. 
per Hour. 



14-3 
12.8 
II. 4 
10.5 
9.8 

9-5 
9.0 



Non-condensing Engines. 



Efficiency 


Pounds of Steam 


T,-T, 


per H. P. 


T^ 


per Hour. 


0.053 


50.9 


0.084 


32.8 


0.124 


22.9 


O.T57 


18.4 


0.186 


16.0 


0.207 


14.6 


0.238 


I3-I 



STEAM-ENGINE, l8l 

Equation (241) shows that the latent heat of evaporation is 
a measure of the amount of work that one unit of weight of a 
vapor can do in an engine ; the larger the latent heat, the more 
the work per pound will be. Equation (240) shows that the 
efficiency does not depend on the latent heat nor on any other 
property of the working substance, as was shown in the second 
law of thermodynamics, of which this is a special case. 

A comparison of Carnot's cycle for the steam-engine in Fig. 
45 with that of Carnot's cycle for an air-engine, Fig. 23, shows 
that the chief difference is that the isothermal for a mixture of 
a liquid and its vapor is a straight line, while that of a gas is a 
hyperbola. In both, the heat is received and rejected during 
isothermal expansion and isothermal compression only. In the 
steam-engine the latent heat of vaporization is the property by 
means of which heat is received and rejected. In the air-en- 
gine the latent heat of expansion plays the same part. The 
fact that the latent heat of vaporization of steam is large, per- 
mits the steam-engine cylinder to be smaller than that of a hot- 
air-engine cylinder, though the true comparison of two such en- 
gines should include the weight and bulk of the whole appara- 
tus, including for the steam-engine the boiler and condenser. 

The old fallacy that the latent heat of vaporization of 
steam is the source of a loss that can be avoided by an engine 
using a substance which, like air, has no change of state, and 
hence no latent heat of vaporization, is apparent. The latent 
heat yielded by the steam to the condensing water is indeed 
large ; but it is an unavoidable loss, and an essential action of 
a heat-engine. 

The Actual Engine. — The cycle of all actual steam-en- 
gines is quite different from Carnot's cycle, and, as will be seen, 
it always has a less efficiency. Steam is generated in a boiler 
at constant pressure, and is carried to the engine through a 
pipe of more or less length, suffering in transit a loss of heat by 
radiation and a loss of pressure from friction. This steam is 
admitted to the cylinder for a portion of the stroke, during 
which time work is done by an isothermal expansion of the 
water and steam in the boiler. At the same time the entering 



1 82 THERMODYNAMICS OF THE STEAM-ENGINE. 

steam yields heat to the walls of the cylinder and suffers partial 
condensation. After a portion of the stroke the supply of the 
steam is shut off, and the steam in the cylinder expands, doing 
work. In general, the walls of the cylinder give heat to the 
water previously condensed, causing a partial reevaporation^ 
though sometimes the walls receive heat during a part or the 
whole of the expansion. Near the end of the stroke the com- 
munication is opened with the condenser, and the steam quick- 
ly falls nearly to the constant pressure maintained in the con- 
denser ; when the expansion is carried so far as to reduce the 
pressure to that of the back pressure, the cycle is complete at 
this part; otherwise, it is incomplete. During the return stroke 
the piston expels the steam in the cylinder to the condenser, 
and the walls yield heat to the steam and water in the cylinder, 
nearly, if not completely, evaporating all the water remaining. 
Towards the end of the stroke the communication with the 
condenser is interrupted, and the steam remaining in the cylin- 
der is compressed, and the temperature and pressure are raised. 
During the compression heat may be yielded by the steam to 
the walls, or conversely, depending on the extent of compres- 
sion, and on whether a steam jacket is used or not. If the com- 
pression be carried so far that the pressure is raised to the ini- 
tial pressure, the cycle is complete at this part; otherwise, it 
is not. Just before the end of the stroke steam is admitted in 
anticipation of the next stroke. 

The water resulting from the condensation of steam in the 
condenser is returned to the boiler by the air-pump and feed- 
pump, thereby forming a closed cycle of operations. The air- 
pump is required to remove the air which enters the boiler with 
the feed-water, and passes with the steam through the engine 
and into the condenser. If there were no air admitted to the 
boiler, engine, or condenser, with the feed-water or by leakage, 
one pump might take the water from the condenser and return 
it to the boiler. When a surface condenser is used, the same 
water is returned to the boiler and used continuously, thereby 
forming a true closed cycle. When a jet condenser is used, 
the steam and condensing water mingle, and are removed to- 



CRANK-EFFORT DIAGRAMS. 1 83 

together similarly placed ordinates of Figs. 108 and 106, we get 
the resulting curve of crank-effort shown in Fig. 109. 

68. Illustration of the Effect of Reciprocating Parts. — 

Fig. no is an indicator-card, from an engine of 12 in. diameter 
of cylinder, 2 ft. stroke, 200 revolutions per minute, weight of 
the reciprocating parts is 470 lbs., and the connecting-rod is six 
times that of the stroke. 

In Fig. Ill the vacuum and compression lines are reversed, 
so that the ordinates between the upper and lower lines give 
the true effective pressures at their respective parts. 

In Fig. 112 the half crank-circle GH is drawn, and divided 
into eight equal parts. The corresponding positions of the 
connecting-rod are next drawn. We now prolong the crank- 
line OE, and erect a perpendicular to the path of the piston, 
intersecting OE at K. Upon KO, from K, is laid off, to the 
same scale as the indicator-card, the value of 

O.oooio'^ \WrEJn 
= Kv. 



w' is then drawn parallel to the corresponding line of the con- 
necting-rod. Now as the velocity of the piston was zero when 
the crank was at OG, Kv' represents, approximately, the mean 
accelerating force between G and E. We now take a crank 
position OM, half-way between OG and OE, and lay off in 
Fig. 113, on the corresponding ordinate, Mm = Kv' . In a 
similar manner, in Fig. 112, we find K'v", and laying off upon 
it the length Kv' , we have v'v" , which is the mean accelerating 
force between E and F. This is laid off in Fig. 113 as Nn, etc. 
We also calculate, by the formulae deduced in the preced- 
ing article, the accelerating forces at the dead-centres, and plot 
them at Aa and Bb, Fig. 113, and through all the points found 
draw the curve amn . . . b. All ordinates below AB are to be 
subtracted, and those above AB added to the pressures shown 
by the indicator, thus producing the final diagram shown in 
Fig. 1 14, which is now ready to be used in finding the curve of 
crank-effort. 



1 84 THERMODYNAMICS OF THE STEAM-ENGINE. 

the exchange of heat between the walls of the cylinder and the 
steam is in no case included in such theories. Rankine* states 
the effect of water in the clearance space, and says that the 
thermal action of the walls of the cylinder has the same effect ; 
but he makes no attempt at an estimation of the effect. Zeuner,f 
in connection with the discussion of the adiabatic curve of a 
mixture of water and steam, admits the thermal action of the 
walls, but asserts that the effect has been over-estimated, and 
that it is slight. He carries his opinion so far as to assert at 
the same place, that in locomotives the water mingled with the 
steam coming from the boiler amounts to from twenty-five to 
thirty per cent of the whole ; that being the percentage re- 
quired to make the adiabatic curve agree with the actual ex- 
pansion curve of the indicator-card. In a problem he assumes 
fifteen per cent of priming. Again, he states that the steam 
in the clearance space is superheated by the compression, as it 
would be, if nearly dry, in a non-conducting cylinder. In later 
writings he has receded in part from this position. 

Comparison with the experimental performance of engines 
shows that these" theories are frequently in error by a large 
amount, which must be due to the neglect of the effect of radi- 
ation and of the thermal action of the walls of the cylinder. 
All investigators from the time of Watt have known that the 
omission of these actions involved an error, and their failure to 
include them in their theories is due, in most part, to the lack 
of experimental data. The theories are to be considered as 
first approximations, without which the existence and amount 
of the error would never have been known ; and the complete 
theory is to be obtained by the insertion of the missing quanti- 
ties in the old theories, which with this exception are correct 
in principle. 

At the present time such a complete theory cannot be 
stated, because the form even of the factors depending on the 
thermal action of the walls has not been discovered, and all at- 
tempts to introduce such factors have led to unsatisfactory re- 

* Steam-engine and other Prime Movers, p. 421. 
f Mechanische Warmetheorie, pp. 421, 486, 499. 



THE STEAM-ENGINE. 1 85 

suits. The proper direction of investigation appears to be to 
determine the thermal action of the walls quantitatively, in en- 
gines of different forms, and working under different conditions, 
so that bad construction and methods of working may be avoid- 
ed, and ultimately a complete theory may be constructed. 
Though a large amount of experimental information exists, the 
larger part cannot be used for this purpose, because the experi- 
ments, though sufficient for the purposes sought by the experi- 
menters, fail to give certain essential data. This, together 
with the complexity of the subject, has made all attempts 
to complete the theory unsatisfactory up to the present time. 

Hirn's Analysis. — The best analysis of the action of the 
steam in the cylinder of an engine is given by Hirn,* and the 
most complete experiments have been made in accordance, by 
his direction or under his inspiration. He calls the old form 
of theories generic theories, while his form he calls the practical 
theory. His method cannot be considered as a complete the- 
ory, since it does not allow us to predict the action of a new 
form of engine. It does, however, enable us to determine the 
real behavior of existing engines. 

The clearest statement of Hirn's theory is derived from 
some memoirs by Zeuner, f in which the equations are de- 
duced by the ordinary methods of thermodynamics, in better 
form than that given by Hirn himself. The memoirs are 
written in criticism of Hirn's methods and conclusions, but the 
equations are accepted by both writers, as 
in fact they must be, whatever the conclu- 
sicins from their application may be. 

Let Fig. 46 represent the cylinder of a 
steam-engine and the diagram of the 
actual cycle without lead of admission or 
release. Let the weight of the mixture of 
steam and water admitted per stroke be \r 
M, of which the part Mx is steam and Fig. 46. 

M{\—x) is water. The condition of the mixture is known 

* Theorie Mecanique de la Chaleur, Tome II. 

f Revue universelle des Mines, vol. xi. p. 15, vol. xiii. p. i. 




1 



J 



1 86 THERMODYNAMICS OF THE STEAM-ENGINE. 

from the pressure /, with which it enters the cyhnder, and 
from X, Let the volume of the clearance be V^ , that of the 
piston displacement up to cut-off be V^ ; let the total piston dis- 
placement be Fj, and the volume to be displaced by the pis- 
ton between compression and the end of the stroke be Fg. 
Let /j,/^ J /a, and/o be the pressures at cut-off, at the end of 
the stroke, at compression, and at admission, while the corre- 
sponding values of x are distinguished by the same subscripts. 
Finally, let the weight of the water and steam in the clearance 
space during compression be M^. 

The heat required to raise M units of weight of water from 
freezing-point to the temperature t corresponding to/, and to 
evaporate the portion Mx, is 

Q = M{<^ + xr) (245) 

For steam superheated to the temperature i^, 

Q = M[q + r + c,{i^-i)] (246) 

The internal heat of the mixture in the clearance space at 
admission is 

At cut-off the internal heat of the mixture in the cylinder is 

During the admission the external work done is W^, and 
the walls of the cylinder have absorbed the heat 2« ; hence 

Q + J/„(?, + ^.A>.) = AW^+Q^ + {M+ >/.) (?. + x,p,). (247) 

In case the steam remains superheated up to the point of 
cut-off, this equation cannot be used, but that condition does 
not commonly occur in practice. As the heat absorbed by the 
walls is given a positive sign, the heat yielded should have the 
negative sign ; but it is more convenient to give the positive 
sign to all, and then in calculation of a problem the numerical 



THE STEAM-ENGINE. 18/ 

values will receive the proper sign to signify in which way the 
heat passes. 

The internal heat of the mixture in the cylinder at the end 
of expansion is 

the external work done is PF^, and the heat yielded by the 
walls of the cylinder is Q^,. As stated above, the numerical 
value of Qt, when heat is yielded has the negative sign ; if heat 
is given to the walls during expansion, which may occur if the 
steam is very strongly superheated, the numerical value is 
negative, but in such case equation (247) cannot be used. 
Since no heat comes from sources outside of the cylinder, 

(>/+ M:, {g, + ^,/3,) = AW, + Q,+ {M +M,) {g, + x,p,). (248) 

During the exhaust the work W, is done by the engine on 
the steam, and the walls of the cylinder yield the heat Q,] the 
heat carried away by the water resulting from the condensa- 
tion of steam in the condenser is Mq^, q^ being the heat of the 
liquid corresponding to the pressure in the condenser ; the 
heat carried away by the cooling water is G((qk — <li) , G being 
the pounds of cooling water per stroke, and qi and q^ the heats 
of the liquid at the initial and final temperatures ; the internal 
heat in the steam caught in the cylinder at compression is 

Combining these equations, we have 

= a + Mq, + G{q, - q>) + M^q, + x^p^^, (249) 

During compression the work done on the steam is W^, and 
the heat transferred to or from the walls of the cylinder is Q^. 
The intrinsic energy at the end of compression is 

^ofe + ^oPo) ; 

.-. Mlq, + x^ft^ -^AlV,= Qa + M,{q, + x,p,). ' (250) 



1 88 THERMODYNAMICS OF THE STEAM-ENGINE. 

The four equations (246) to (250) enable us to determine 
the interchange of heat during each operation of the cycle, 
provided that a sufficient number of data can be obtained 
experimentally. The indicator-card furnishes means of deter- 
mining the work done by or on the steam in each operation, 
and also gives the pressures from which the values of q and p 
can be found. The weight J/ may be determined by weighing 
the feed-water or else the condensed steam, when a surface 
condenser is used. The weight of cooling water must be de- 
termined by direct measurement; also the temperature t^, 4, 
and ti must be observed directly. If the entering steam *is 
moist, X must be determined by a calorimeter experiment ; if it 
is superheated, t^ may be observed by a thermometer in the 
steam-pipe near the engine. The values remaining are J/^, x^, 
x^, x^, and x^ . 

The specific volume of a mixture of steam and water is 

V ^ XU -{- <T \ 

or, since the volume occupied by the water in the cylinder is 
small compared with that occupied by the steam, 

V ^z xu, and V ^=^ Mxu (251) 

If desired, the exact value of v may be carried into the 
equations, but at the expense of a complication which does not 
seem necessary in the present state of the subject. 

From equation (251), 

^o^o^o= K; (252) 

^0-^3^^3=f^o+^3; . (253) 

(J/+J/„K^/,= F„+F,; (254) 

(lf + J/„K^/,= F„+F, (255) 

Substituting in equations (246) to (250), and solving, for the 
quantities of heat interchanged between the steam and the 
walls of the cylinder, we have ' 



THE STEAM-ENGINE. 1 89 

a=e+^^.?.-(V)/+Vl/.k+F. J -(F.+ F.) -J -^ fF,; (256) 
a=(vI/+^.)(!7 -?,)+( f'.+ f^of; -(;^.+ !^,)5 -^ W,- (257) 

-(f".+ i^.)J + ^w^.; (258) 

a = 7f/.fe-?,) + (f^o+!^=)|-f".5 + ^f^- • • • (259) 

In these last four equations the only quantity on the right- 
hand side which is not determinable by direct observation is 
M^ . These equations assume that the steam is always in equi- 
librium, or that the energy due to velocity, eddies, and commo- 
tion is inappreciable. 

To determine M^, Hirn makes the assumption that x^ is 
unity, or that the steam is dry at the beginning of compression. 
In some other experiments, in which the compression is small 
and the vacuum good, he assumes that M^ is so small that it 
may be neglected. The first assumption is one commonly 
made, and the second cannot cause much error under the con- 
ditions given, if the first is allowable. Zeuner points out that 
if M^ is taken too small, the equations deduced will show a 
much greater apparent action of the walls than really occurs, 
and he states that the assumption of a sufficiently large value 
of M^, i.e., of a large enough arriount of water in the clearance, 
will make the terms Q^, Qb, Qc and Q^ very small. 

The total work deduced from the indicator is 

W=W,+ W,-W,-W, (260) 

If the heat lost by radiation during one stroke is Qg and 
that furnished by condensation of steam in the jacket is Qjy 
then 

a + a + G. + a = a-<2/ (261) 



190 THERMODYNAMICS OF THE STEAM-ENGINE. 

Adding the equations (256) to (259), member to member, 
and using equations (261) and (260), we have 

Q.-Qj=Q-Mq,~G{q,-q^-AW,. . (262) 

which might have been written directly, since it is apparent 
that if we subtract from the heat supphed the heat rejected 
and the heat changed into work, the remainder is the heat lost 
by radiation. When the heat supplied by the jacket is greater 
than that lost by radiation, both sides of equation (262) be- 
come negative. Again, Qj is zero when a jacket is not used. 

Equation (262) gives a method of calculating the heat lost 
by radiation, a quantity which can be determined directly only 
when a steam-jacket is used, and which is then subject to un- 
certainty. It is, however, to be remarked that the equation 
(262) determines Q^ by subtraction, and therefore it is affected 
by the accumulated error of the experiment, which may be much 
larger than the uncertainty of a direct determination when a 
jacket is used. 

If Qe and Qj are determined directly, then equation (261) is 
another equation of condition, so that by its aid equations 
(251) to (259) may be solved for M^ ; or what is more conven- 
ient, the equation (262) may be used as a check on the equa- 
tions for determining the quantities of heat Q^, Qb, Qc and 
Qa, and thus the assumption made in determining M^, i.e., :v^ = 
I, may be tested. 

The storing of the heat Qa and the restoring of heat g^, 
both at a varying temperature, are productive of a loss of 
efficiency ; but the most serious, loss is due to the direct loss of 
the heat Q^, which is thrown into the condenser without com- 
pensation. In many engines, Q^ is the most serious cause of 
low efficiency ; it is frequently several times as large as all the 
heat changed into work. Hirn has proposed to make Q^ a 
measure of the advantage of various devices, such as super- 
heating, steam-jackets, compounding, etc. 

The equations are deduced for an engine having a surface 
condenser ; for one having a jet condenser, g^ and ^^ become 
identical. For a non-condensing engine equation (258), con- 



THE STEAM-ENGINE, I9I 

taining quantities depending on the condenser, cannot be used, 
but by aid of equation (262) those quantities may be ehmi- 
nated, giving 

a = {M + M^q, - M,q, + ( f; + F,) 1^ - ( F. + V,) g 

-Q-Qi^Q.^A{W^W:), (263) 

which may be used for a non-condensing engine, provided that 
Q^ and Qj are both determined by direct observation. 

Hirn has used both equation (258) and equation (263) for 
determining Q,, to which he attaches so much importance, and 
thereby obtains a check on his work. The check is, of course, 
equivalent to determining Q^^ the heat of radiation by equa- 
tion (262), as well as by direct observation. Or the comparison 
of results by the two methods may be considered to show the 
combined error of, first, the observations, and, second, the 
method of calculating the steam caught in the clearance space. 
Hirn's original work and that of his school is stated in the 
numerical solution of special problems ; consequently the real 
meaning of the check from the two methods of calculation is 
not so clearly presented, and the coincidence of results, from 
apparently independent methods, is more striking than in the 
discussion just given. 

In certain very important experiments by Hirn and by 
Hallauer, the compression was nearly if not quite absent, 
which, with the low absolute pressure in the condenser, made 
J/„, calculated by the usual method, so small, that it was neg- 
lected. This reduced equations (258) and (263) to 

a = M{q, - ^.) - G{q^ - q) + ( F. + F,) ^} + AW,. . (264) 
Q, = J/^, + ( F. + V,) ^;- -Q-Q.+ Q, + A{ W+ W,). (265) 

The result by equation (264) was considered to be the direct 
result, and that by equation (265) the proof of the correctness 
and accuracy of the theory and experiment. The numerical 
calculation involved some minor differences which could not 
seriously affect the result. When the amount of the back 



192 



THERMODYNAMICS OF THE STEAM-ENGINE. 



pressure, or of the compression, forbade the use of these equa- 
tions, a method nearly equivalent to equations (262) and (263) 
was employed. 

Problem. — The following are the data of a test made on 
a Harris-Corliss engine in the laboratory of the Institute of 
Technology, together with the calculation of the results : 
Diameter of the engine, .... 8 inches 

Stroke, 2 feet 

Piston displacement: crank end,. . 0.6791 cu. ft. 

head end, . . 0.7016 " 
Clearance, per cent of piston displacement : 

crank end, 3.75 

head end, 5.42 

Boiler-pressure by gauge, .... 77.4 pounds 

Barometer, 14.8 " 

Condition of steam, one per cent of moisture. 
Events of the stroke : 

Cut-off: crank end, 0.306 of stroke 



head end, .... 


. 0.320 '^ 


Release at end of stroke. 




Compression : crank end, . . 


. 0.013 of stroke 


head end, . . 


. 0.0391 '' 


Duration of the test, one hour. 




Total number of revolutions, . . 


. 3692 


Weight of steam used, .... 


548 pounds 


Weight of condensing water used, 


. 14,568 '' 


Temperatures : 




Condensed steam, 


. /,= i4i°.iF. 


Condensing water : cold, . . 


. t,= 52°.9F. 


warm, . . 


. 4= 88°.3F. 



ABSOLUTE PRESSURES, FROM INDICATOR-DIAGRAMS, AND 
CORRESPONDING PROPERTIES OF SATURATED STEAM. 





Crank End. 


Head End. 




P 


9 


P 


u 


P 


9 


P 


u 


Cut-off 

Release 

Compression. . 
Admission 


83.6 
29.2 
14.8 
21.8 


284.6 
217.8 
181. I 
201.5 


813.0 
864,8 
893.2 

877-4 


5.190 
13.924 

26.464 

18.344 


83.3 
31-9 
14.8 
29.8 


284.4 
222.9 
181. 1 
219.0 


813.2 
861.8 
893.2 
863.9 


5.207 
12.804 
26.464 
13.664 



THE STEAM-ENGINE. 



193 



MEAN PRESSURES, AND HEAT EQUIVALENTS OF EXTERNAL 

WORKsT 





Crank End. 


Head 


End. 




Mean Pressures. 


Equivalents of 
Work. 


Mean Pressures. 


Equivalents of 
Work. 




87-7 
44-5 
14.8 
18.3 


3-369 
3-877 
1-836 
0.0299 


89-3 
47-1 
14.8 
21.8 


3-7II 
4-159 
1.847 
O.IIO4 


Expansion 


Exhaust 


Compression 





VOLUMES. CUBIC FEET. 



At cut-off, To + Fi 

At release, Fo -|- V-i 

At co.mpression, Vq -\- F3. 
At admission, V^ 



Crank End. 



0.2333 
o . 7046 

0.0343 

0.02550 



Head End. 



0.2626 
0.7396 
0.0655 
0.03806 



At the boiler-pressure, 92.1 pounds absolute, we have 

r = 888.4, q — 291.7. 

The steam used per stroke is 
548 



M^ 



2 X 3692 



0.0742 pounds. 



The steam caught in the clearance space at compression, on 
the assumption that the steam is then dry and saturated, is 
obtained by multiplying the mean volume at that point by the 
weight of one cubic foot of steam at the pressure at compres- 
sion ; 



0.0343+0.0655 



0.0021 pounds ; 



2 26.464 

M -\- M^ — 0.0742 + 0.0021 = 0.0763 pounds. 

The condensing water used per stroke is 

G = — ^-7 — = 1.973. 
2 X 3692 ^'^ 

Q = M{xr -\-q) — 0.0742(0.99 X 888.4 + 291.7) = 86.903 ; 



194 THERMODYNAMICS OF THE STEAM-ENGINE. 

1 

= 86.903 + 0.0021 X i(20i.5 + 219.0) — 0.0763 X 284.5 

1/ 813.0 , ^ ^ 813. 2\ 3.369+3.711 

- - (0.2333 X — ^— + 0.2626 X — ^- - ^ ^ ^^-^^ 

I 2 V ^^^ 5.19 ' 5.207/ 2 

= 86.903 + 0.441-21.707 + 1.815-38.778-3.540 = 25.134; 

^ / 222.9 + 217. 8\ , ^ 

= 0.763(^284.5 ^"i^^-j + 38.778 

1/ . 864.8 , . 86i.8\ 3-877+4.159 

— 0.7046 X — - — h 07396 X — ^- — ^^ 

2\ ^ ^ 13.924 ' ^ 12.804/ 2 

= 4.898 + 38.778 - 46.771 - 4.018 = - 7.1 13 ; 

a = (^/+^o)^.-^0^3+(^0+^.)fj-(^0+^3)g-^^. 

222.0 + 217.8 
= 0.0763 X --^ — — 0.0021 X 1 8 1. 1 +46.771 

0.0343+0.0655 893.2 
-^ ^ X ^ - °-°742 X 109.3 

, , 1.836+ 1.847 
- i-973(56-3 - 21.0) -{ 7 

= 16.809 — 0.380 + 46.77— 1.684 — 8. 1 10 — 69.644+ 1-841 
= -14-397; 

/ 201.5 + 2I9.0\ , 

= 0.0021 (^181.1 -^ — ^-j + 1.684 - I.8I5 

0.0299 + 0.1 104 

' 2 

= — 0.061 + 1.684 — 1.8 1 5 +0.070= —0.122 ; 

(2.+G.+G.+2^=25. 134-7.113-14-397-0.122=3.502 = a. 



THE STEAM-ENGINE. 1 95 

Also, equation (262) for this case gives 

Qe^Q-Mq,-G{q,-q:)-AW 

= 86.903 - 8. 1 10 — 69.644 — (3.735 + 3.846 — 1.841 — 0.070) 
= 86.903 — 8.1 10 — 5.647 = 3.502. 

It is to be remembered that the heat lost by radiation and 
conduction per stroke, when estimated in this manner, is 
affected by the accumulated errors of observation and compu- 
tation, which may be a large part of the total value of Q^ as 
determined. 

Dropping superfluous significant figures, we have in B. T. U. 

Q=:S6.g, a=24.9, & = 6.9, 0,= i4.4, Qd=-o.i2, Qe^S-S- 
The horse-power of the engine is 

77^5.670 X 3692 X 2 ^ ^^ 

60 X 33000 ^-^ 

and the steam per horse-power per hour is 

548 
Y5;^j== 33.5 pounds. 

A consideration of the theory just elaborated will show that 
the true condition of the steam at compression is of great im- 
portance. Zeuner shows that for some of Hallauer's experi- 
ments an assumption that M^ = J/ will reduce Q^ to zero. In 
reply Hirn shows that such an assumption does not reduce the 
other quantities, Q^, Qi, , and Q^, to zero, as ought to be the 
case if there is no interchange of heat between the cylinder and 
the steam ; and Hallauer shows that the behavior of the steam 
during compression cannot be accounted for on such an as- 
sumption. Again, the condition of the exhaust steam may be 
calculated in some experiments by considering the condenser 
to be a calorimeter, and such a calculation gave about six per 
cent of water. If the steam in the cylinder at compression 
had the same amount of water, the error of considering it dry 



196 



THERMODYNAMICS OF THE STEAM-ENGINE. 



would be small. Moreover, water which collects in the cold 
cylinder of an engine when started, quickly passes away, as is 
indicated by the change of the sound of exhaust from dull and 
heavy to dry and short. All this shows that a large quantity 
of water in the clearance space is improbable if not impossible, 
but it does not entirely justify the assumption that the steam 
is dry at compression. Experiments made on engines having 
a large compression may give light on the subject. 

Surface Condensers. — The proper discussion of condens- 
ers can be given only in connection with the theory of the 
steam-engine, though it is commonly treated as a separate 
problem. 

Let Fig. 47 represent the cylinder of a steam-engine and a 
surface condenser. The piston is at the end of the stroke, and 

the cylinder contains M pounds of a 
mixture of steam and water, having 
the conditions determined by t^ and 
x^. The cylinder by the opening of 
the exhaust-valve is put in communi- 
cation with surface condenser con- 




tammg 



a weight M^ of steam and 



Fig. 



water, having the condition deter- 
mined by t^ and x^ . We may im- 
agine the process to be divided into 
two parts : (i) the steam and water 
in the cylinder and condenser min- 
gle, and are reduced to the temperature t^ ; (2) the piston 
passes to the other end of the stroke and reduces the volume 
from F;+F,to F,. 

The result would be the same if we imagine the steam in 
the cylinder (i) to be reduced to the temperature t^ before the 
exhaust-valve opens, and then (2) after the valve opens to be 
reduced from the volume V^ -\- V^ to V^ . 

In the first process the steam and water is reduced, at con- 
stant volume, from the temperature t^ to t^. To find the heat 
abstracted, we have 

dQ = M.AdE 



M,\_dq^d{xfS)\ 



THE STEAM. EXGINE. I97 

But X^U^ -{- a- = xu -\- a- ; 

.•.e. = ^.[?. -?, + ^A(f;-|)]- • • (266) 

At the end of this process we have a volume V^ -\- V^ of 
steam and water having a weight M, -{- M^ = M, and having a 
value x^' that could be found if desired. 

The second process reduces the volume from F^ -|- V^ to V^ , 
and the value of x changes again and becomes ;r/^ The heat 
abstracted is 

Mr,ix:-x,") (267) 

The volumes before and after compression are 

K+K = M{x:u, + <r) ; 

SO that the change of volume is 

V, = Mulx: - x;'). 
But, from the initial condition, ^ 

V, = M^x^u, + 0-) ; 
so that, if 0- be neglected, 

« - -^/ ) 

Substituting this in equation (267), we have for the heat 
abstracted during the second process, 



M. 



■,u,^^M,x,u\^^Ap) (268) 



The total heat withdrawn during both processes is, there- 
fore, 

M\.^.-g. + ^ip. + Ap,u,)-] (269) 



198 THERMODYNAMICS OF THE STEAM-ENGINE. 

But during the exhaust from the cyHnder of an engine the 
walls yield to the steam and water contained the heat Q,, and 
this passes into the condenser, so that the total heat to be car 
ried away by the cooling water is 

a+[^/.^.-^.+^.(P: + ^A^:)]. . . . (270) 

Each unit of weight of cooling water in passing through the 
condenser will acquire q^— qi units of heat ; consequently the 
pounds of cooling water for one pound of mixture of water and 
steam drawn from the cylinder will be 

j^ + ^x - ^. + ^.{P. + ^A^O 

(271) 

qk — qi 

If it be assumed that — y = o, that jr^ := i, and that Ap^u^ is 
the same as Ap^u^ , then the expression becomes 
^1 - ^. + ^1 K — q. 



qk — qi qk 



(272) 



The expression commonly used for calculating the cooling 
water required is 

A-/ 



in which /I is the total heat of steam at the pressure in the ex- 
haust pipe. 

The expression is deduced by assuming that the exhaust 
steam is dry and saturated, and that it is condensed and cooled 
to the temperature t^ by the cooling water, which thereby gains 
the temperature 4 — ti • 

Some experiments by Hallauer^ on a condensing-engine 
using saturated and superheated steam, show that the exhaust 
steam in that engine contained from 6 to 12 per cent of mois- 
ture. Experiments in the laboratory of the Institute of Tech- 

* Bulletin de la Soc. Ind. de Mulhouse, vol. xlvii. 1877. 



THE STEAM-ENGINE, I99 

nology, on non-condensing engines, show in general a less 
amount of moisture in the exhaust steam. It may be concluded 
that exhaust steam from an engine is seldom or never super- 
heated, that it usually contains a moderate amount of moisture, 
and that it is sufficient to assume it to be dry and saturated, 
for calculation of the condensing water required. 

Cooling Surface. — Experiments on the quantity of cooling 
surface required by a surface-condenser are few and unsatisfac- 
tory, and a comparison of condensers of marine engines shows 
a wide diversity of practice. Seaton* says that with an initial 
temperature of 60°, and with 120° for the feed-water, a conden- 
sation of 13 pounds of steam per square foot per hour is con- 
sidered fair work. A new condenser in good condition may 
condense much more steam per square foot per hour than this, 
but allowance must be made for fouling and clogging, especially 
for vessels that make long voyages. 

Seaton also gives the following table of square feet of cooling 
surface per indicated horse-power : 



olute terminal 


pressure, 


Square feet 


pounds per sq, 


, in. 


per I.H.P. 


30 


. 


3 


20 




2.5 


15 




2.25 


124 




2. 


10 




1.8 


8 




1.6 


6 




1-5 



For ships stationed in the tropics, allow 20 per cent more ; 
for ships which occasionally visit the tropics, allow 10 per cent 
more ; for ships constantly in a cold climate, 10 per cent less 
may be allowed. 

Jet Condenser. — In the jet condenser the cooling water 
mingles with the steam, and the final temperatures of both be- 
come tf,. There are some minor differences that appear in the 
exact expression for the cooling water required from that for 



* Manual of Marine Engineering. 



2CX) THERMODYNAMICS OF THE STEAM-ENGINE. 

surface condensers ; but the difference is slight, and in any case 
the simple expression 

Qk— qt 

is to be preferred in practice. 

The capacity of a jet condenser should not be less than one 
fourth of that of the cylinder or cylinders exhausting into it, 
and need seldom be more than one half. One third of the 
capacity of the cylinder or cylinders is generally sufficient. 

Designing Engines. — The only question that is properly 
discussed here is the probable form of the indicator-diagram, 
which gives immediately the method of finding the mean effec- 
tive pressure and, consequently, the size of the cylinder of the 
engine. 

The most reliable way of finding the expected mean effec- 
tive pressure in the design of a new engine is to measure an 
indicator-card from an engine of the same or similar type and 
size, and working under the same conditions. 

As it can hardly be expected that a diagram of exactly the 
required form will be at hand, a diagram like Fig. 48 may be 
drawn, using the proper cut-off, compression, 
and clearance. If an indicator-card taken 
from an engine under similar conditions is 
attainable, it may be used to determine ex- 
^^^^^^^^^^^ — ponential equations for the expansion and 
'^' '^^* compression curves ; usually the exponent 

will be different for the two curves, and must be determined 
separately. For ordinary work it is sufificient to use the hyper- 
bola for both curves, and to assume the steam line a and the 
back-pressure line c to be parallel to the atmospheric line, while 
the lead of admission and exhaust may be neglected. It is 
also customary to assume a loss of pressure of one or two 
pounds between the boiler and the engine, and a back pressure 
of a like or greater amount above the pressure in the condenser 
or the pressure of the atmosphere, as the case may be. 

If the diagram is drawn to scale, the area and mean effec- 




THE STEAM-ENGINE. 20I 

tive pressure may be found by measuring it ; or, the form of 
the expansion and compression curves being assumed, the areas 
under the steam hne, the expansion curve, the back-pressure 
hne, and the compression curves may be calculated separately, 
integrating between limits when necessary, and therefrom the 
resulting area of the diagram and the mean effective pressure 
may be determined. Ordinarily, the expansion and compres- 
sion curves are assumed to be hyperbolae. 

Seaton* gives the following multipliers for finding the mean 
effective pressure from that calculated by the process described: 

Multipliers for Finding Probable M. E. P., Simple Expansive Engine • 



(i) Special valve-gear, or with separate cut-off valve, 
engine jacketed 

(2) Good ordinary valves, large ports, engine jacketed. 

(3) Ordinary valves and gears as in general practice, 

un jacketed. . 



0.94 
0.9-0.92 

0.80-0.85 



To estimate the consumption of steam, we may calculate 
from the pressure and volume at release the weight of steam 
then present in the cylinder, and in a similar manner the 
weight of steam caught in the clearance space from the volume 
and pressure at compression, both under the assumption that 
the steam is dry and saturated. The difference is the steam 
exhausted per stroke under the assumption ; but to get a fair 
estimate of the probable consumption, it is necessary to add a 
fraction of this amount, depending on the style and size of the 
engine and on the conditions under which it is to run. Suffi- 
cient data for this purpose seldom exist ; so it is customary to 
add to the calculated amount one fourth to one third of itself, 
to get the probable consumption of non-condensing engines of 
medium size. 

Problem. — Required the dimensions of an engine to give 
100 horse-power ; revolutions, 120; gauge-pressure^ 80 pounds ; 
cut-off at \ stroke ; release at end of stroke ; compression at yiy 
stroke, and clearance 5 per cent. 

* Manual of Marine Engineering. 



202 THERMODYNAMICS OF THE STEAM-ENGINE. 

Assuming hyperbolic expansion and compression gives for 
the mean effective pressure 



0.333 X 927 + 0.383 X 92.7 log. ^^ - 16 X 0.9 

— 0.15 X 16 log, -^ =: 49.5 pounds, 

if the pressure during admission is 78 pounds, and during 
exhaust is 1.3 pounds above the atmosphere. 

If, further, the stroke of the engine is twice the diameter, 
then 

Ttd'' 2d 

X ^- X 120 X 2 X 495 



4 12 
100 = — ^ 



33000 

.-. d = 12.85, ^ = 25.70. 

The volume of the cylinder will be 1.93 cubic feet, and the 
terminal pressure will be 33.8 pounds absolute. At 33.8 pounds 
the density of steam is 0.08234, and at 16 pounds it is 0.04067. 
The consumption of steam per horse-power per hour, on the 
assumption of dry steam at release and compression, will be 

(0.082 34 X 1 .05 —0.04067 X 0. 1 5) 1 .93 X 2 X 1 20 X 60 
= 22.3 pounds. 

100 ^ ^ 

If one third of this quantity be added, then the estimated 
consumption of steam will be 30 pounds per horse-power per 
hour. 

The calculated dimensions are stated in inches and hun- 
dreds, but in practice the engine would be made I2-| inches in 
diameter by 25f inches stroke ; or possibly the dimensions 13 
by 25 would be chosen, since they give nearly the same 
volume. 



THE STEAM-ENGINE, 203 



EXAMPLES. 

1. Find the volume of the cyHnder of a double-acting steam 
engine to give lOO H.P. at 60 revolutions per minute. Assume 
it to run on Carnot's cycle, to have 150 pounds by the gauge, 
and 1.5 pounds absolute for the maximum and minimum pres- 
sures, and to have the steam dry and saturated at the begin- 
ning of the adiabatic expansion. 

2. In problem i, make the minimum pressure 14.7 pounds. 

3. Suppose an actual steam-engine, working between the 
same pressures as in Example i, to use 18 pounds of steam per 
hour, and to run without compression. Find the volume of the 
cylinder if the steam at release contains 20 per cent of moisture. 

4. Find the relative sizes of cylinders of perfect heat-engines 
using water, ether, and carbon tetrachloride, and working be- 
tween the temperatures of 100° C. and 10° C. 

Suggestion : Find the work of Carnot's cycle for one kilo- 
gram ; find the relative weights to give equal quantities of 
work, and thence the relatives volumes. 

5. Find relative sizes in Example 4 when working between 
the pressures of 5 atmospheres and \ of one atmosphere. 

6. Make calculations for Hirn's analysis for the experiments 
given on pages 305 and 334. 

7. Find the weight of cooling water for a hundred horse- 
power engine using 20 pounds of steam per horse-power per 
hour, the vacuum in the condenser being 26 inches of mercury, 
the temperature of the condensed water being 120° F., and the 
temperatures of the cooling water being 60° F. and 110° F. 

8. In Example 7, find the area of cooling surface for a sur- 
face condenser, the terminal pressure being \2\ pounds. 

9. Calculate the problem given on page 201, assuming as 
the equation of the expansion curve 

pif'^ _ const., 

and for the compression curve 

pv'-^ — const. 



CHAPTER XIII. , 

COMPOUND ENGINES. 

In a compound engine, steam is admitted from the boiler 
into a small cylinder, from which it is exhausted above atmos- 
pheric pressure. The steam is then admitted to a large cylin- 
der, from which it passes to a condenser. If we assume that 
the steam from the small cylinder is exhausted into a large 
receiver, the back pressure in that cylinder and the pressure 
during the admission to the large cylinder will be uniform. If, 
further, we assume that there is no clearance in either cylin- 
der, that the back pressure in the small cyhnder and the for- 
ward pressure in the large cylinder are the same, and that the 
expansion in the small cylinder reduces the pressure down to 
the back pressure in that cylinder, the diagram for the small 
cylinder will be ABCD, Fig. 49, and for the large cylinder 
DCEFG. The volume in the large cylinder at cut-off is equal 
to the total volume of the small cylinder, since the large cylin- 
der takes from the receiver the same weight of steam that is 
exhausted by the small cylinder, and, in this case, at the same 
pressure. 

The case just discussed is one extreme. The other extreme 
occurs when the small cylinder exhausts directly into the large 
cylinder without an intermediate receiver. In such engines the 
pistons must begin and end their strokes together. They may 
both act on the beam of a beam engine, or they may act on 
one crank or on two cranks at 180° apart. 

For such an engine, ABCD, Fig. 50, is the diagram for the 
small cyhnder. The steam line and expansion line AB and BC 

204 



COMPOUND ENGINES. 



205 



are like those of a simple engine. When the piston of the 
small cylinder begins the return stroke, communication is 
opened with the large cylinder, and the steam passes from one 
to the other, and expands to the amount of the difference of 
the volume, it being assumed that the communication remains 
open to the end of the stroke. The back-pressure line CD for 



p 








X" 


\ 






D 


\ 


^ 




■0- 




E 
















psr 



Fig. 49. 



Fig. 



the small cylinder, and the admission line HI for the large 
cylinder, gradually fall on account of this expansion. The dia- 
gram for the large cylinder is HIKG, which is turned toward 
the left for convenience. 

To combine the two diagrams, draw the Hne abed, parallel 
to V'OV, and from b lay off dd equal to ca ; then d is one point 
of the expansion curve of the combined diagram. The point 
C corresponds with H, and E, corresponding with /, is as far 
to the right as / is to the left. 

For a non-conducting cylinder, the combined diagram for a 
compound engine, whether with or without a receiver, is the 
same as that for a simple engine, which has a cylinder the 
same size as the large cylinder of the compound engine, and 
which takes at each stroke the same volume of steam as the 
small cylinder, and at the same pressure. The only advantage 
gained by the addition of the small cylinder to such an engine 
is a more even distribution of work during the stroke, and a 
smaller initial stress on the crank-pin. 

Compound engines may be divided into two classes — those 
with a receiver and those without a receiver ; the latter are 
called " Woolf engines" on the continent of Europe. Engines 
without a receiver must have the pistons begin and end their 



206 THERMODYNAMICS OF THE STEAM-ENGINE. 

strokes at the same time ; they may act on the same crank or on 
cranks i8o° apart. The pistons of a receiver compound engine 
may make strokes in any order. A form of receiver compound 
engine with two cyHnders, commonly used in marine work, has 
the cranks at 90° to give handiness and certainty of action. 
Large marine engines have been made with one small cylinder 
and two large or low-pressure cylinders, both of which draw 
steam from the receiver and exhaust to the condenser. Such 
engines usually have the cranks at 120°, though other arrange- 
ments have been made. 

In reality, all compound engines have a receiver, or a space 
between the cylinders corresponding to one, and in no case is 
the receiver of sufficient size to entirely prevent fluctuation of 
pressure. In the later marine work the receiver has been made 
small, and frequently the steam-chests and connecting pipes 
have been allowed to fulfil that function. This contraction of 
size involves greater fluctuation of pressure, but for other rea- 
sons it appears to be favorable to economy. 

Compound Engine without Receiver. — The indicator- 
cards from, a compound engine without a receiver are repre- 
sented by Fig. 51. The steam line and ex- 
pansion line of the small cylinder, AB and 
BC, do not differ from those of a simple 
engine. At C the exhaust opens, and the 
steam suddenly expands into the space be- 
tween the cylinders and the clearance of 
Fig. 51. ^]^g large cylinder, and the pressure falls 

from C to D, During the return stroke, the volume in the 
large cylinder increases more rapidly than that of the small 
cylinder decreases, so that the back-pressure line DE gradually 
falls, as does also the admission line HI of the large cylinder, 
the difference between these two lines being due to the resist- 
ance to the flow of steam from one to the other. At E the 
communication between the two cylinders is closed by the cut- 
off of the large cylinder ; the steam is thus compressed in the 
small cylinder and the space between the two cylinders to /% 
at which the exhaust of the small cylinder closes ; and the 




COMPOUND ENGINES. 



207 




remainder of the diagram FGA is like that of a simple engine. 
From /, the point of cut-off of the large cylinder, the remain- 
der of the diagram IKLMNH is like the same part of the dia- 
gram of a simple engine. 

The " drop" CD at the end of the stroke of the small cylin- 
der, and the difference between the lines DE and HI, are evi- 
dent losses of efficiency. The compression EFG for the small 
cylinder, and the accompanying independent expansion IK in 
the large cylinder, are losses of power in the engine ; but tne 
compression, as in a simple en- 
gine, fills the waste spaces, and 
in this case mitigates the effect of 
the " drop." It is apparent that 
there would be a loss of efficiency 
in compounding a non-conducting 
engine, yet under proper circum- 
stances experiment shows an ad- 
vantage in compounding engines 
with metallic cylinders. 

Fig. 52 is a diagram taken from 
a compound pumping-engine at 
the Lawrence, Mass., water-works. 

Compound Engine with Receiver. — In the receiver com- 
pound engine with cranks at 90° the cut-off is commonly later 
than half-stroke, which gives rise to a species 
of double admission. The diagrams for the 
small and large cylinders are represented by 

Fig. 53. 

When the exhaust of the small cylinder 
begins, the large piston is at about half- stroke, 
and communication then exists through the receiver between 
the two cylinders. The cut-off of the large cylinder closes this 
communication, and the back pressure rises in the small cylin- 
der until, at about half-stroke, the admission to the other end 
of the large cylinder makes the back pressure fall, down to the 
compression in the small cylinder. 

The admission to the large cylinder begins at about half- 



FlG. 




Fig. 




208 THERMODYNAMICS OF THE STEAM-ENGINE. 

stroke of the small piston, with a free communication be- 
tween the two cylinders, till the compression begins in the 
small cyhnder. The steam in the receiver then expands with 
diminishing pressure to about half-stroke, when exhaust at the 
other end of the small cylinder begins, causing an increase of 
pressure for the remainder of the admission. 

Fig. 53<2: gives diagrams from the high and low pressure 
cylinders of a receiver compound engine 
of the yacht Gleam. 

The diagrams from three cylinder 

compound engines, and from other ar- 

^ ^^ 7 rangements, have pecuHarities that must 

^^^.-^ I be investigated separately for each case. 

-/— J— All will show a drop at the end of the 

" expansion in the small cylinder, and in 

iG. S3«. general a loss of pressure between the 

small and large cylinders. 

A comparison with the ideal diagram, Fig. 49, will show a 
loss of efficiency from the drop, and the loss of pressure be- 
tween the small and large cylinders, and yet, as with the 
Woolf engine, compounding under proper circumstances is an 
advantage. 

It is customary to attempt the comparison of the expan- 
sion in a compound engine to that of a simple engine by an 
adaptation of the methods of Figs. 49 and 50, making allow- 
ance for the clearance and the action of the receiver and of 
the compression. More or less complication is introduced to 
meet the difficulties arising, yet the result is not satisfactory. 
The simplest method, which applies to receiver compound 
engines, is a modification of Fig. 49. The diagrams are trans- 
ferred to a common scale, and referred to the same axis of 
pressure and volume, each being set off to the right of the 
axis OP by the amount of its own clearance. It is customary to 
complete the process by drawing a rectangular hyperbola in a 
manner similar to that used for a simple engine. 

The whole process is of doubtful utility, the more espe- 
cially as there appears to be no reason to assume the hyperbola 



COMPOUND ENGINES. 209 

or any other simple curve to represent the actual equivalent 
expansion in a simple engine. The several gaps that appear 
in such a combined diagram, due to drop, loss of pressure and 
compression, seem to show a loss as compared with a simple 
engine, which may or may not exist. The only way of know^ 
ing anything about the performance of a type of engine is to 
make a series of careful tests upon it. 

Triple and Quadruple Compound Engines. — The same 
influences which introduced the compound engines, when the 
common steam-pressure changed from forty to eighty pounds 
to the square inch, have brought in the successive expansion 
through three cylinders, the high-pressure, intermediate, and 
low-pressure cylinders, now that 125 to 170 pounds pressure 
are employed. Just as three or more cylinders are combined 
in various ways for compound engines, so four, five, or six cylin- 
ders have been arranged in various manners for triple com- 
pound engines ; for example, a compound engine v/ith two 
cylinders may be conveniently changed into a triple compound 
engine by the addition of a small high-pressure cylinder over 
each of the existing cylinders. 

Quadruple engines with four successive expansions have 
been employed with high-pressure steam, but with the advis- 
able pressures for present use, the extra complication and fric- 
tion make it a doubtful expedient. 

Horse-power of Compound Engines. — For the first 
approximation it is customary to calculate the horse-power of 
a compound engine of any sort, as if the total expansion 
occurred in the cylinder or cylinders that exhaust into the 
condenser; and it is assumed that the expansion curve is a 
rectangular hyperbola. 

Problem. — Let the boiler-pressure be 80 pounds by the 
gauge, or 94.7 pounds absolute ; let the back pressure be 4 
pounds absolute; and let the total number of expansions be six, 
so that the volume of steam exhausted to the condenser is six 
times the volume admitted from the boiler. Neglecting the effect 
of clearance and compression, the mean effective pressure is 

94.7 X J + 947 X \ log^ f - 4 X I = 40.06 = M.E.P. 



2IO THERMODYNAMICS OF THE STEAM-ENGINE. 

If the large cylinder is 30 inches in diameter, and the stroke 
is 4 feet, the horse-power at 60 revolutions per minute is 

—~ X 40.06 X 2 X 4 X 60 -^ 33000 = 412 H.P. 

Point of Cut-off. — Let the ratio of the volumes of the high 
and low pressure cylinders of a compound engine be R, let the 
number of expansions in the small cylinder be e, and let the 
total number of expansions be E ; then 

E = eR\ {27z) 

E 
^ = :^- (274) 

Problem. — Let the ratio of the cylinders of the engine dis- 
cussed in the preceding paragraph be 3 ; with the same stroke 
the diameters will be ij^-^ and 30 inches. The number of ex- 
pansions in the small cylinder will be J, and the cut-off for that 
cylinder will be at ^ of the stroke. 

The cut-off in the large cylinder has an effect on the distri- 
bution of the work and the adjustment of the maximum pres- 
sure on each piston, but it does not affect the preliminary cal- 
culation of mean effective pressure and horse-power. 

Ratio of Cylinders. — In designing compound engines, 
more especially for marine work, it is deemed important for 
the smooth action of the engine that the total work shall be 
evenly distributed upon the several cranks of the engines, and 
that the maximum pressure on each of the cranks shall be the 
same, and shall not be excessive. In case two or more pistons 
act on one crank, the total work and the resultant pressure on 
those pistons are to be considered ; but more commonly each 
piston acts on a separate crank, and then the work and pressure 
on the several pistons are to be considered. 

If it is desired that the work shall be equally divided be- 
tween the two cylinders of a receiver compound engine, the 
ratio of their volumes may be found as follows. Let the initial 
pressure be/, the receiver pressure/,, and the pressure in the 



COMPOUND ENGINES. 211 

condenser zero ; then, on the assumption that the volumes are 
inversely as the pressures, 

E 
P^'P^^-Rp^ ^^^^) 

Let V be the volume of the small cylinder and Fthat of the 

large cylinder ; then the works done in them may be assumed 

to be 

V 
-p{iJ^\og,e)-vp, and -j^p,{i + \og,R). 

V 
Equating these quantities and substituting v for -5 , 

Again, substituting for e and / from equations (274) and 
(275), and reducing, 

log,^=: i+2log,i?; 

log,,^- 0.4343 
•'-^^^-^= 5:8686 • • • • : (^7^) 

If it is desired to make the maximum pressure on the pis- 
tons the same, then we should have 

pa^pA. (277) 

a and A being the areas of the small and large pistons respec- 
tively. If the stroke is the same for the two pistons, then the 
volumes are proportional to the areas, so that equation i?.*]"]^ 
becomes 

pv — py\ 

V 
or, substituting for/ from equation (275), and for — its value Ey 

R' = E (278) 

Applied to the problem stated above, the ratio of the vol- 



212 THERMODYNAMICS OF THE STEAM-ENGINE. 

umes of the cylinders for six expansions is 2.49 by equation 
(276) and 2.45 by equation (278). 

The method of equation (276) assumes that there is no drop 
to the receiver ; a larger ratio will be accompanied by a drop, 
and a smaller ratio will cause the steam in the small cylinder 
to be expanded to a lower pressure than that in the receiver. 

In practice both the ratio of the cylinders and the total 
expansions are assumed, and then the distribution of work and 
the maximum loads on the crank-pins are calculated, allowing- 
for clearance and compression. Designers of engines usually 
have a sufficient number of good examples at hand to enable 
them to assume these data. In default of such data it may be 
necessary to assume proportions, to make preliminary calcula- 
tions, and to revise the proportions till satisfactory results are 
obtained. For compound engines using 80 pounds of steam 
pressure, the ratio is 1:3 or 1:4. For triple expansio^n en- 
gines the cylinders may be made to increase in the ratio i : 2 
or I : 2\. 

Calculations for Compound Engines. — Instead of de- 
ducing equations for the calculations for compound engines, a 
few problems will be solved to exhibit the method. 

Example i. — Boiler-pressure 80 pounds by the gauge, re- 
ceiver-pressure 18 pounds, pressure in the condenser 4 pounds 
absolute. Ratio of the cylinders, 3 ; total expansion, 6. Clear- 
ance, 10 per cent for the small cylinder and 8 per cent for the 
large cylinder. Compression at 0.15 of the stroke for each 
cylinder. 

First Solution. — An approximate solution, neglecting clear- 
ance and compression, will first be made. 

The cut-off in the small cylinder will be at 

|. = 1 stroke. 

The terminal pressure in the small cylinder, on the assumption 
of hyperbolic expansion, will be 

80 + 14.7 n u 1 ^ 
= 47-35 pounds absolute. 



COMPOUND ENGINES. 213 

The drop to the receiver will be 

47-35 - (15 + 14.7) ^ 17-65 pounds. 

The cut-off in the large cylinder is determined by the con- 
dition that it must draw the same weight of steam per stroke 
from the receiver as is delivered to it by the small cylinder. 
The volume v is discharged by the small cylinder per stroke, 
which may be assumed to expand to the volume 

47.35 

V 

29.7 

in the receiver on account of the drop. The cut-off in the 
large cylinder is therefore at 

IZlli v^V ^ "^^'^^ = 0.509 of the stroke. 
29.7 29.7 X 3 

The mean effective pressure in the small cylinder is 

94.7 X 4-(i + log. 2) - 29.7 = 50.47. 
The mean effective pressure in the large cylinder is 

29.7 X 0.509 [i + log, ^-— j - 4 = 20.03 pounds. 

The mean effective pressure reduced to the large cylinder is 

50.47 

\- 20.03 = 36.85 pounds. 

This result may be compared with the result obtained on 
page 209, on the assumption that all the work was done in the 
large cylinder, i.e., 40.06 pounds. 

The division of work between the two cylinders is in the 
ratio 

50.47 I 



3 X 20.03 1.2 



214 THERMODYNAMICS OF THE STEAM-ENGINE. 

The drop to the receiver might be reduced by shortening 
the cut-off of the large cylinder, but such an arrangement 
would produce a greater inequality in the distribution of work. 
On the other hand, the work will be more equally distributed 
with a longer cut-off on the large cylinder, but that would give 
a larger drop and a more wasteful engine. 

The maximum pressure on the small piston is 

94.7 — 29.7 = 65.0 pounds, 

equivalent to 

65.0 

= 21.7 pounds 

on the large piston. 

The maximum pressure on the large piston is 

29.7 — 4 = 25.3 pounds. 

Lengthening the cut-off of the large cylinder will increase 
the pressure on the small piston and diminish that on the 
large piston. 

Second Solution. — A more complete solution with slightly 
different results can be given, taking account of clearance and 
compression. ^ 

The cut-off in the small cylinder will be taken at one-half 
stroke, as before. 

The terminal pressure is 

94.7 X 0.60 ,^ 111. 

= 51.00 pounds absolute. 

1. 10 -^ ^ 

The drop to the receiver is 

51.66 — 29.7 = 21.96 pounds. 
The cut-off for the large cylinder is at 

51.66 



297 X 3 



0.5798 of the stroke. 



COMPOUXD ENGINES. 21 5 

The mean effective pressure in the small cylinder is • 

94.7 X i + 947 X 0.6 log,^ - 29.7 X 0.85 

- 29.7 X 0.25 log.^^ = 53-65 pounds. 

The mean effective pressure in the large cylinder is 

1.08 
29.7 X 0.5798 -h 29.7 X 0.6598 log-^ ^^g - 4 X 0.85 

0-23 

- 4 X 0.23 log, ^^ = 22.51 pounds. 
The mean effective pressure reduced to the large cylinder is 
+ 22.51 = 40.39 pounds. 



53.65 



3 

The division of work between the two cylinders is in the 
ratio 

53-65 ^ I 
3 X 22.51 1.26* 

The maximum pressures on the small and large pistons are 
the same as calculated before. 

Example 2. — Let the data of Example i be taken for a 
non-receiver compound engine. For such an engine the only 
effect of the cut-off on the large cylinder is to produce a com- 
pression in the small cylinder and the space between the two 
cylinders corresponding to the receiver of a receiver engine. 
Let the cut-off on the large cylinder occur at 0.70 of the stroke. 
Let the volume of the intermediate space be o. 10 of the dis 
placement of the large cylinder, or 0.30 of the volume of the 
small cylinder. 

The terminal pressure in the small cylinder, as in the second 
solution of Example i, is 51.66 pounds absolute. 



2l6 THERMODYNAMICS OF THE STEAM-ENGUSFE. 

When the exhaust-valve opens, the steam from the small 
cylinder mingles with that in the intermediate space and in the 
clearance space of the large cylinder, and a drop occurs. The 
steam caught by the compression in the clearance of the large 
cylinder has so small a density that it may be neglected. The 
effect of the steam in the intermediate space may be esti- 
mated in the following manner. Disregarding the steam in 
the intermediate space, the volume i.io?:^ of steam at the ter- 
minal pressure 51.66 may be assumed to occupy the volume 

(0.3 + o.\)v + 0.1 F + (0.7 + 0.08) V = 3.042; 

at the cut-off of the large cylinder, and the corresponding pres- 
sure is 

51.66 X I.I o 

= 18.7 pounds. 

3.04 ^ ^ 

After the cut-off occurs the steam in the small cylinder at 
this pressure is compressed from the volume 

(0.3 + o. 1)2; + o. I F =r o.yv, 
which it then occupies, to the volume 

0.1 F+ OAv — 0.4^, 

and the final pressure will be 

0.7 
18.71 X — = 32.7 pounds. 

The pressure in both cylinders after the drop has occurred 
may be assumed to be 

32.7 X 0.1 F+ 51.66 X 1. 1^ 66.64 

r-7— ' — i mTT — = — z~ = 40-6 pounds. 

i.i^ + (o.i +o.o8)F 1.64 ^ ^ 

The drop is 

51.66 — 40.6= I I.I pounds. 



COMPOUND EXGINES. 21/ 

The corrected pressure at cut-off of the large cylinder 
will be 

66.64 



3 -04 



21.9 pounds, 



instead of 18.7 pounds given above, and it appears unnecessary 
to make a second approximation. 

The mean forward pressure on the small piston is 

947 X i +94.7 X 0.6 log, ^ == 85.7 pounds. 

The back pressure on the small piston and the forward 
pressure on the large piston up to the cut-off of the large 
cylinder is 

3.04 
40.6 X 1.647^ log,— ^ -^ o.y{V— v) = 29.4 pounds. 

The back pressure on the small piston from the cut-off of 
the large cylinder to the end of the stroke is properly divided 
into two parts, the first part ending at the compression of the 
small cylinder, during which steam is compressed in the small 
cylinder and its clearance and the intermediate space, and the 
second part from the compression to the end of the stroke, 
during which steam is compressed in the small cylinder and its 
clearance only. For our present purpose it is sufficient to 
make the calculation on the assumption that the compression 
of the small cylinder is at the end of the stroke, which gives 
for the back pressure of this part of the stroke of the small 
piston 

0.7 
21.9 X o.yv log, — -^ 0.32^ = 28.6 pounds. 
0.4 

The mean back pressure on the small piston is therefore 

0.7 X 29.4 + 0.3 X 28.6 = 28.2 pounds. 



2l8 THERMODYNAMICS OF THE STEAM-ENGINE. 

The mean effective pressure on the small piston is 

85.7 — 28.2 = 47.5 pounds. 

The forward pressure on the large piston from cut-off to the 
end of the stroke is 

21.9 X 0.78 log, — g -^ 0.3 = 18.5 pounds. 

The mean forward pressure on the large piston is 

29.4 X 0.7 + 18.5 X 0.3 = 26.1 pounds. 
The mean back pressure on the large piston is 

4 X 0.85 + 4 X 0.23 log, ^ = 4.1 pounds, 

and the mean effective pressure on the same is 

26.1 — 4.1 = 22 pounds. 

The mean effective pressure reduced to the large cylinder is 

47.5 

+ 22 == 37.8 pounds. 

The division of work between the two cylinders is in the 
ratio 

47»3 ^ I 
3 X 22 1.4' 

The maximum pressure on the small piston occurs at 0.3 of 
the stroke when the back pressure is a minimum, and is then 

94.7-21.9 = 72.8, 

which is equivalent to a pressure on the large piston of 

72.8 

=r 24.3 pounds. 



COMPOUND ENGINES. 219 

The maximum pressure on the large piston is about 35 
pounds. 

If the two pistons are fixed to one rod, the maximum pres- 
sure, reduced to the large piston, is about 60 pounds. The 
maximum pressure on the piston of a simple engine using the 
same steam-pressure and expanding the same number of times 
will be 90.7 pounds per square inch. 

The drop may be made smaller, or if desired it may be 
made to disappear, by shortening the cut-off of the large cylin- 
der, and experiments show that a gain of efficiency accompa- 
nies such a change. 

Example 3. — If the engine were made with a receiver and 
with two low-pressure cylinders, each with its own crank, the 
drop could be avoided, and a good distribution of the work 
among the three cylinders could be attained. The clearance 
and compression will be neglected in this solution. 

The terminal pressure in the small cylinder, as in the first 
solution of Example i, is 47.35 pounds absolute, and this is 
also the back pressure in that cylinder. 

The mean effective pressure in the small cylinder is 

94.7 X \{\ -f log, 2) - 47.35 ^ 42.82 pounds. 

To compare this with one of the low-pressure cylinders this 
result may be divided by |-, giving 28.55 pounds. 

The cut-off of each of the low-pressure cylinders must be at 
\ stroke. 

The mean effective pressure in each of the low-pressure 
cylinders is 

47-35 X i(i -f log, 3) - 4 = 25.79 pounds. 

There is no drop, and the equivalent mean effective 
pressure reduced to one low-pressure cylinder is 

42.83 

f- 25.79 — 40.06 pounds, 

as found on page 209. 



220 THERMODYNAMICS OF THE STEAM-ENGINE. 

Example 4. — A triple-expansion engine using steam at 150 
pounds gauge-pressure has the volumes of the cylinders in the 
ratio I '.2^\6\\ and the cut-off is at 0.6 of the stroke on the 
high-pressure and intermediate cylinder and at 0.75 of the 
stroke on the low-pressure cylinder. 

Neglecting the effects of clearance and compression, the 
total expansion is 

^X6i=io.4; 
the pressure in the first intermediate receiver is 

0.6 X 2.5 ^ ^ ' 

and the pressure in the second intermediate receiver is 
164.7 X 0.6 



0.75 X 6.25 



21.08 pounds 



while the pressure in the condenser may be taken at 4 pounds 
absolute. 

The mean effective pressure in the high-pressure cylinder is 

164.7 X 0.6f I + log, ^j - 65.88 = 83.41 pounds. 
The mean effective pressure in the intermediate cylinder is 

65.88 X o.6f I -f log, — ^j — 21.08 = 38.64 pounds. 
The mean effective pressure in the low-pressure cylinder is 
21.08 X 0.75(1 +log, -^ —4= 16.36 pounds. 



COMPOUND ENGINES.- 221 

The distribution of work among the three cyhnders is in 
the proportion 

83.41 38.64 ^ ^ 
-#-^ : ~ — - : 16.36 :: I : 1.16 : 1.23. 
6.25 2.5 ^. ^ 

The pressures on the crank-pins are in the proportion 

164.7-65.88 65.88-21.08 

--^ ^ : -^ : 21.08 — 4 '-'- I : i-H : 1.08. 

6.25 2.5 ^ ^ 

The drop to the first intermediate receiver is 
164.7 X 0.6 — 65.88 = 32.94 pounds. 

The drop to the second intermediate receiver is 

65.88 X 0.6 — 21.08 = 12.45 pounds. 

On account of the loss of pressure between the boiler and 
the engine, and between the engine and the condenser, and of 
the resistance of valves and passages, the mean effective pres- 
sure calculated as in the preceding examples, taking account 
of clearance and compression, is not realized in practice. The 
following table of multipliers is given by Seaton * for finding 
the probable mean effective pressure of compound marine en- 
gines : 

MULTIPLIERS FOR FINDING PROBABLE M.E.P. COMPOUND 

ENGINES. 



(i) Expansion-valve to H.P. cylinder, large ports, cylinders jacketed. 

(2) Ordinary slide-valves, good ports, cylinders jacketed 

(3) General practice of merchant service, early cut-off in both cylin- 

ders, without expansion-valves or jackets 

(4) Fast-running engines of type and design usually fitted in war 

ships 



o.g-0.92 
0.8-0.85 

o . 7-0 . 8 

0.6-0.8 



To find the probable mean effective pressure, by aid of this 
table, the mean effective pressure for each cylinder is to be calcu- 
lated separately, allowing for clearance and compression, and the 
result multiplied by the proper factor. Or the equivalent mean 

* Manual of Marine Engineering. 



222 THERMODYNAMICS OF THE STEAM-ENGINE, 

effective pressure, as calculated in the examples, allowing for 
clearance and compression, may be multiplied by the factor. 

A fair approximation to the probable mean effective pres- 
sure of marine engines of the ordinary type can be obtained by 
calculating the mean effective pressure approximately, on the 
assumption that the total expansion takes place in one cylin- 
der, not allowing for clearance and compression, and then mul- 
tiplying successively by 0.96 and by the proper factor from the 
table. 

Hirn's Analysis. — Since the admission to the high-pres- 
sure cylinder and the exhaust from the low-pressure cylinder of 
a compound engine do not differ from the corresponding parts 
of the cycle of a simple engine, we may apply the equations 
deduced for the simple engine to the determination of the 
value of Q,, the heat rejected from the walls of the cyHnder to 
the condenser. 

Hirn and Hallauer, in all of their work, content themselves 
with determining explicitly this one of the four quantities, Q^, 
Qi,, Q,, and Q^, but there appears to be no reason why the 
other three should not be determined also, for compound en- 
gines as well as for simple engines, provided a clear idea is 
obtained of their meanings. Q^ is the heat absorbed by the 
walls of the high-pressure cylinder during the admission of 
steam to it ; Q^ is the heat rejected to the condenser by the 
walls of the low-pressure cylinder during its exhaust ; and Q^ 
is the interchange of heat during the compression in the large 
cylinder. Qi, appears as the heat yielded by the walls of the 
cylinders during expansion, but it is an incomplete expression 
for a complicated operation. During the expansion in the 
small cylinder heat is yielded by its walls to the mixture of 
water and steam ; also during the exhaust heat is yielded by 
the walls of the small cylinder, so that nearly if not all the 
water present is vaporized as during the exhaust of a simple 
engine. In the large cylinder the steam is condensed on the 
walls during the first part of the admission for a Woolf engine, 
and probably up to cut-off for a receiver compound engine, and 
heat is consequently absorbed by the walls of that cylinder, 



COMPOUND ENGINES, 223 

but that heat is given up in large part during the expansion in 
the remainder of the stroke. The final result is a yielding of 
heat to the mixture in the cylinder. In good types of com- 
pound engines the value of Q, is small, though there may be a 
large interchange of heat during the earlier operations, and 
this fact is the probable explanation of the good efficiency of 
such engines. 

Of the four quantities of work found in the equations for 
finding the interchange of heat, W^, is the absolute work dur- 
ing admission to the small cylinder, W^ is the negative work of 
the back pressure, and W^ the negative work of the compres- 
sion for the large cylinder. Wj, is the total work of expansion 
which may be obtained by the expression 

w^ W^+ w,+ w,+ w,. 

Hallauer does not state clearly how Wj, is obtained in the 
work which he gives for compound engines. 

The following method is proposed as an extension of 
Hirn's theory to compound engines, with the hope that by its 
aid the transfer of heat from the walls of the small cylinder to 
the walls of the large cylinder, with kindred phenomena, may 
be calculated after proper experiments are made. 

The method can be applied when each cylinder has its own 
jacket with separate drain, so that the condensation in each 
and the radiation from each can be determined separately, and 
when, further, all the data from the condenser can be obtained. 
For the high-pressure cylinder, as for a non-condensing simple 
engine, we have 

a= 0+ M,g,-{M-^M,)g,+ F. ^ - ( l\+ V) j^ ~ AW. (273) 

Hq 14'. 

Q,={M+M,){q-g:,-\-{V,+ V) ^-{K+ V,) ~-AW,. (274) 
Q,={M+M:)g-M,gM V.+ K) ^} -(F.+ V,) ^ 

-Q-Qj+Q.+A{w+w:). (275) 
Q,=MXg-g:)+{V,+ V,)^'~V,^+AW, (276) 



224 THERMODYNAMICS OF THE STEAM-ENGINE. 

For the low-pressure cylinder the heat received during 
admission, Q\ cannot be obtained directly, but it can be ob- 
tained by aid of equation (264), which may be written 

Q'=Q:-QJ-^Mq:-YG{3:-ql)^AW' ; (277) 

and the four required equations may be written 

a= Q:-Q!^M:q:^Mq:-{M^M:)q-G{<i.- ?,) 

a=(Jl/+J//)(?/- ?,')+( F/+F/) ^, 

-{V:+V:)^-AW;; . (279) 
Q-(M+M:)q,'-M:q,'-Mq:- Giq,-q,) 

+( K'+ K') ^ -{K'+ V:) j! +A W: ; . (280) 

Q, = MJ{q,'-q:)+{K'+V:)^-K'^+AW/. . . (281) 

With triple and quadruple expansion engines the following 
method may be used. The heat rejected by the high-pressure 
cyhnder during exhaust is 

Q+Qj-AW-Q,. 

This heat passes into the first intermediate cylinder, and from 
thence with the gain or loss experienced there proceeds to the 
next cylinder. The sum, or difference, may be taken for Q\ 
the heat brought into that next cylinder per stroke. The same 
operation may be applied to each successive cylinder, and the 
result may be checked by the data depending on the condenser. 



CHAPTER XIV. 

TESTING STEAM-ENGINES. 

Tests of steam-engines are made either to find the cost of 
power or to study the transformations of heat and work in the 
engine, though both objects are frequently sought in the same 
test. The cost of power is commonly stated in pounds of coal, 
or of combustible, per horse-power per hour. To obtain this 
cost of power the engine and boiler must be considered as one 
system, and a test consists essentially in weighing the coal 
consumed and measuring, in some manner, the work produced 
in a given time. The power may be measured by aid of steam- 
engine indicators, by a friction brake, or by a transmission 
dynamometer ; the measurement of the fuel consumed must be 
done with all the precautions required for an accurate boiler 
test, and such a test should last at least ten hours. Though a 
test of this kind will give directly the cost of power of a plant 
consisting of engine, boiler, etc., or will determine which of 
two or more plants is the most economical, it does not give the 
means of distinguishing whether the excellence or defects of a 
system are due to the engine or the boiler, much less does it 
enable us to make such an analysis as will show why a given 
engine or boiler is better than another. 

To distinguish between the performance of the engine and 
of the boiler, it is customary to state the performance of the 
boiler in pounds of water evaporated per pound of fuel, and 
that of the engine in pounds of water per horse-power per 
hour. The evaporative efficiency of a boiler is frequently 
stated in pounds of water evaporated per pound of fuel, from 
and at 2X2° F. ; that is, a special thermal unit, equal to 965.8 
B.T.U., is employed. For example, if a boiler, for each pound 
of fuel consumed, takes eight pounds of feed-water at 60° F., 

225 



226 THERMODYNAMICS OF THE STEAM-ENGINE. 

and evaporates it into dry steam under a pressure of lOO 
pounds to the square inch above the atmosphere, then it 
is assumed that each pound of fuel can evaporate 

8x1184.9 

pounds of water at 212° F., and under the pressure of the 
atmosphere. No attempt has been made to put the steam 
consumption of engines on as logical a basis, and in general it is 
necessary to know the type of an engine and the conditions 
under which it works in order to judge whether its perform- 
ance is good or not. 

It is in general better to make an engine test independent 
of the boiler test, especially if an attempt is to be made to ana- 
lyze the transformations of heat and work ; and this is the more 
convenient as an engine test of from one to four hours in 
length is sufficient under favorable conditions. Even though 
the immediate object of the test is to ascertain the steam con- 
sumption only, as many as possible of the data mentioned 
in Hirn's analysis, page 185, should be taken and recorded : to 
wit, the pressure and condition, whether primed or super- 
heated, of the steam supplied to the engine, together with the 
weight of the same ; the weight and initial and final tempera- 
tures of the cooling or injection water, and, where a surface con- 
denser is used, the temperature of the water resulting from the 
condensation of the steam ; the vacuum in the condenser and 
the pressure of the atmosphere ; where the engine is com- 
pounded, the pressure of the receiver or receivers, when nearly 
constant, may be taken, and if in any way heat is added to or 
taken from the steam in a receiver, such heat should be meas- 
ured if possible ; if any cylinder or cylinders have steam-jack- 
ets, the pressure and condition of steam supplied to each jacket, 
and the weight and temperature of the water condensed 
therein, should be known ; indicator-diagrams should be taken 
at each end of each cylinder, at intervals depending on the 
length and regularity of the test ; the total area of the indica- 
tor-diagrams should be measured, and also the areas, down to 



TESTING STEAM-ENGINES. 22/ 

the line of absolute vacuum, under the lines of admission, to 
cut-off, expansion, exhaust, and compression. When an engine 
is steam-jacketed, it is assumed that the condensation in the 
jacket or jackets when the engine is at rest is a measure of 
the loss by external radiation, conduction, etc. 

Thermometers. — Temperatures are commonly measured 
by aid of mercurial thermometers, of which three grades may be 
distinguished. For work resembling that done by the physic- 
ist the highest grade should be used, and these must ordinarily 
be calibrated, and have their boihng and freezing points deter- 
mined by the experimenter or some qualified person ; since 
the freezing-point is liable to change, it should be redetermined 
when necessary. For important data good thermometers must 
be used, such as are sold by reliable dealers, but it is pref- 
erable that they should be calibrated or else compared with 
a thermometer that is known to be reliable. For secondary 
data or for those requiring little accuracy, common thermome- 
ters with the graduation on the stem may be used, but these 
also should have their errors determined and allowed for. Ther- 
mometers with detachable scales should be used only for crude 
w^ork. 

Gauges. — Pressures are commonly measured by Bourdon 
gauges, and if recently compared with a correct mercury col- 
umn, these are sufficient for engineering work. The columns 
used by gauge-makers are commonly subject to minor errors, 
and are not usually corrected for temperature. It is important 
that such gauges should be frequently retested. From their 
convenience, vacuum gauges of the same form are used, even 
where a mercurial gauge could easily be applied. 

The pressure of the atmosphere may be taken with either a 
mercurial or an aneroid barometer, but if the latter is used its 
errors must be known. It should be easy to make the baro- 
metric errors only a fraction of the unavoidable gauge errors. 

Dynamometers. — The standard for measurement of power 
is the friction brake. For smooth continuous running it is es- 
sential that the brake and its band should be freely lubricated 
with oil, and that the cooling should be done by a stream of 



228 THERMODYNAMICS OF THE STEAM-ENGINE. 

water that does not come in contact with the rubbing surfaces. 
Sometimes the wheel is cooled by a stream of water circulating 
through it, sometimes the band is so cooled, or both may be. 
A rubbing surface which is not cooled should be of non-con- 
ducting material. 

To avoid the increase of friction on the brake-bearings due 
to the load applied at a single brake arm, two equal arms may 
be used with two equal and opposite forces applied at the ends 
to form a statical couple. 

With care and good workmanship a friction brake may be 
made an instrument of precision sufficient for physical investi- 
gations, but with ordinary care and workmanship it will give 
results of sufficient accuracy for engineering work. 

All forms of transmission dynamometers should be stan- 
dardized, and should have their errors determined by compari- 
son with a friction brake. 

Indicators. — Our knowledge of the errors of indicators,, 
whether of kind or degree, is very limited. Preliminary ex- 
periments seem to show that at moderate speeds, i.e., those 
that give little or no oscillation of the piston and pencil motion, 
the largest errors are due to backlash and pencil friction. The 
latter may be reduced by making the pencil pressure light, but 
there is no remedy for the former. It probably does not intro- 
duce an error of more than one or two per cent in the diagrams 
taken with good indicators. 

It is essential that the reducing motion should be correct, 
and that the indicator-cord should be short. The communica- 
tion between the indicator and the cylinder should be short 
and direct, but if a pipe must be used it should be well 
wrapped to avoid radiation. 

Scales. — Weighing may be done with scales adapted to the 
load. They should be tested with standard weights. 

Weirs and Orifices. — When possible, the quantities of 
water involved in an engine test should be weighed directly ; and 
by proper provision of large tanks and scales, and with large 
valves, large quantities of water may be thus determined. 
When the water cannot be weighed directly it may be meas- 



TESTING STEAM-ENGINES. 229 

ured in tanks of which the volume is known either from meas- 
urement or, preferably, by filling them with weighed water. 

When the two preceding methods do not apply, the water 
may be allowed to flow over a weir or through an orifice, and 
the volume and weight may be determined by the usual 
hydraulic methods. If the weirs or orifices are small, the co- 
efficients of flow should be determined by direct experiment. 

Steam Consumption. — The steam consumption of an engine 
is preferably determined by condensing the exhaust steam in a 
surface-condenser and weighing or gauging the resulting water. 
A great advantage is that a test an hour or two long is then 
sufficient. 

When the exhaust steam cannot be thus condensed the 
boiler or boilers supplying the engine may be isolated so that 
all the steam made must go to the engine, and then the feed- 
water supplied to the boiler may be weighed or gauged. Af- 
ter the engine has been running long enough to come to its 
normal condition, the height of the water in the boiler gauge- 
glass may be noted, all the feed-water during a test of from 
two to four hours in length may be weighed or measured, and 
at the end of the test the water in the gauge-glass must be 
brought to the initial height. 

Calorimeters. — When superheated steam is supplied to an 
engine it is sufficient to take the temperature of the steam in 
the steam-pipe near the engine. When moist steam is used, 
the condition of the steam must be determined by a calorimet- 
ric experiment. Four kinds of calorimeters will be described 
out of a large number that have been used by different experi- 
menters and at different times. They are the barrel calorime- 
ter, the Barrus continuous water calorimeter, the Barrus super- 
heated steam calorimeter, and the throttling calorimeter. 

The Barrel Calorimeter. — A wooden barrel set on scales 
is provided with a large valve for emptying it, and provision is 
made for filling it with cold water, usually from a hydrant pipe, 
and for bringing the steam to be tested. Some form of stirrer 
must be used, a good form being a wooden propeller-wheel on 
a wooden shaft with a hand crank. 



230 THERMODYNAMICS OF THE STEAM-ENGINE. 

The method of making a test is as follows : The barrel is 
weighed empty, and a suitable quantity of cold water is run in 
and weighed. The temperature of the cold water should be 
taken as it enters. The steam-pipe usually terminates in a 
piece of rubber hose which may be swung into or out of the 
barrel. When the barrel is nearly filled with cold water, the 
steam-valve may be opened until all condensed water is blown 
from the pipe and the hose is warmed up ; then the hose may 
be swung into the barrel and steam may be run into the water 
till a proper amount is condensed. A preliminary calculation 
will determine the proper weights of water and steam to give a 
good range of temperatures in the calorimeter. After the 
steam is run in, the water in the barrel maybe well stirred, and 
the highest temperature taken as the final temperature. 

To eliminate the action of the wood of the barrel, one or 
more tests are made and rejected, and the times of running in 
water and steam are made equal, so that the barrel which is 
already warmed by the preceding test may give up as much 
heat during one part of the process as it receives during the 
other part. 

If the pressure of the steam is/, and the part of each pound 
of the mixture which is steam is represented by x, while the 
initial and final temperatures of the water are t^ and Z^? and 
the weights of the water and steam are W and w, then 

w(xr + q-q^= W{q, - q,) ; 

^,^^^W{q^-q:)-w{q-q.) ^ ^ ^ 

wr ^ ^ 

r and q being the latent heat and heat of the liquid for the 
pressure/, and q^ and q^ being the heats of the liquid for the 
temperatures t^ and t^. 

Example. — Suppose that i8o pounds of water at the tem- 
perature of 60°. 2 F. are run into a barrel calorimeter, and that 
the final temperature of the water in the calorimeter is 103°. 6 
F., after 7J pounds of steam at 73.8 pounds by the gauge are 



TESTING STEAM-ENGINES. 23 1 

run in and condensed. At an absolute pressure of 88.5 
pounds, r = 890.4, q = 288.8 ; the heats of the Hquid at 60°. 2 
and I03°.6 are 28.32 and 71.6. 



180(71.6 - 28.32)- 7.25(288.8 - ;i.6) 

X = — 0.903 , 

7.25 X 890.4 



consequently the per cent of priming is 3.7. 

It is to be remarked of this kind of calorimeter that satis- 
factory results are difficult to attain even when every care and 
precaution are used, and that a small error in determining the 
weight of steam, which is obtained by subtraction, makes a 
large difference in the result. 

Barrus Continuous Water Calorimeter. — The difficulty 
of obtaining the weight of steam with sufficient accuracy, which 
occurs in the use of the barrel calorimeter, is avoided in the use 
of the continuous water calorimeter represented by Fig. 54. 
This calorimeter is essentially a small surface condenser of 
special form, so arranged that the condensed steam is weighed 
separately from the cooling water. 

Steam is brought to the calorimeter by the pipe/, with the 
gauge i for giving the pressure. The pipe a, which forms the 
condensing surface, and which may conveniently be made of 
brass pipe one inch in diameter, should have the joints, above 
and below, clear of the bucket containing the cooling water. 
Steam is let into the pipe a at full boiler-pressure, and the con- 
densed water gathers in the pipe below, where the water-level 
is shown at e. The height of the water at e is kept constant 
by aid of the valve at d, which may have a long wooden handle 
attached for convenient regulation. At h there is a thermome- 
ter to determine the temperature of the condensed steam. Since 
this temperature is only a little less than that due to the boiler- 
pressure, the condensed water should be led through a cooler 
like a simple surface condenser, with a separate stream of cool- 
ing water, and the cooled water may be collected and weighed 
on suitable scales. 



232 



THERMODYNAMICS OF THE STEAM-ENGINE, 



The cooling water for the calorimeter is brought by the 
pipe b with a valve for regulating the supply, and is led away 
to a barrel on scales by the pipe <;, with a valve to regulate the 



COLD WATER 




CONDENSED 
WATER 



Fig. 54- 



height of the water in the bucket. To insure a good circula- 
tion and a proper mingling of the cooling water the current is 
directed through a rubber hose to the bottom of the inner cylin- 
der around the pipe a, thence up and into the top of the outer 
cylinder, thence down and out at the bottom of this cylinder 



TESTING STEAM-ENGINES. 233 

and over a weir at the exit. The temperatures of the coohng 
water at entrance and exit are taken by the thermometers / and 
g, which should be rehable to ^^^ of one degree Fahrenheit. 

The pipe/ leading to the calorimeter and the pipe contain- 
ing the condensed steam should be well wrapped as far as to 
the valve at d. At k there is a brass cone to protect the cover- 
ing of the pipe from water. 

Though not essential, it is convenient to line the bucket 
with sheet metal. 

In preparing for a test the water and steam are let on and 
properly regulated, and the calorimeter is allowed to run till 
all parts may be assumed to be at a constant temperature ; the 
cooling water from c and the condensed steam are then directed 
into the receptacles for weighing, and the time is noted as the 
beginning of the test. The steam-pressure and the several tem- 
peratures are taken at intervals and recorded. At the end of 
half an hour or an hour the cooling water and condensed water 
are diverted from the weighing receptacles, and the time is noted 
as the end of the test. The quantities of the cooling and con- 
densed water can be weighed at the end of the test, or the test 
may be made continuous for any desired length of time by hav- 
ing two weighing receptacles for each, and filling and empty- 
ing them alternately. 

The radiation in thermal units per hour must be determined 
by running the calorimeter without cooling water and with the 
bucket filled with hair-felt. 

In this or any form of calorimeter that is capable of giving 
accurate results it is essential that the steam-pressure should 
not change during a test, since a considerable change of pres- 
sure will vitiate the results on account of the heat absorbed or 
yielded by the pipes leading to the condenser. 

Let W a.nd w be the weights of the cooling water for the 
test, and let / be the steam-pressure, and t^ the final tempera- 
ture of the condensed steam taken by the thermometer at h, 
while /j and t^ are the initial and final temperatures of the cool- 
ing water; finally, let the radiation during the test be e thermal 
units. 



234 THERMODYNAMICS OF THE STEAM-ENGINE, 

Then 

w{xr + ^ - ^3) = ^(^2 - ^1) + ^ ; 



\ X ^=^ 



wr 



(283) 



Example. — The following are the data of a test made in the 
laboratory of the Institute of Technology : 



Initial temperature of cooling water 
Final 

Temperature of condensed steam, 
Pressure of the atmosphere, 
Pressure of steam by gauge. 
Duration of test, .... 
Radiation per hour, . . . 
Weight of cooling water, . 
'' *' condensed water, 



37°.49 F. 
83°.84 F. 
304°.88 F. 

14.8 lbs. per sq. in. 

72.4 " " " '' 

40 minutes. 
180B.T. U. 
573.5 pounds. 

29.89 '' 



^ 5;3>5(5i-9i - 5-53) + 120 - 29.89(287.6 - 274.4) 
29.89 X 891.2 



;i; = 0.988. 

Per cent of priming, 1.2. 

It is apparent that any surface condenser may be used in 
the same manner, as a. calorimeter, except that it is not usually 
convenient to fill such a condenser with steam at boiler-pres- 
sure. Since the wire-drawing of steam in a well-wrapped valve 
is accompanied with little loss of heat, this need not interfere 
with such a use of a condenser. In an engine test the quality 
of exhaust steam flowing to either a jet or a surface condenser 
can be determined by equation (282) or (283), except that the 
external radiation cannot always be satisfactorily determined. 

Barrus Superheated-steam Calorimeter. — A form of 
calorimeter devised by Mr. Barrus is shown in Fig. 55, which 



TESTING STEAM-ENGINES. 



235 



determines the quality of steam by finding how much heat is 
required to superheat it. 

The steam to be tested comes into the pipe H and passes 
through a tubular superheater/^, and flows out of an orifice at 



SJEAM TO BE TESTED 
i PIPE 




Fig. 55. 

M. A separate stream of steam comes 
in by the pipe E^ is strongly super- 
heated by gas lamps in the super- 
heater G, passes around the tubes of 
the superheater y, and flows out of an 
orifice at TV of the same diameter as 
that at M. Temperatures are taken 
by the thermometers at ^, ^, and C\ 
and the boiler-pressure, which is admit- 
ted to all the apparatus, is measured 
by a gauge. In the calculation it is as- 
sumed that the specific heat of super- 
heated steam at all temperatures and pressures is Cp = 0.48 as 
determined by Regnault, and that the same weight of steam 
will flow out of each of the orifices M and N under the same 




ORIFICE i DIA. 



236 THERMODYNAMICS OF THE STEAM-ENGINE. 

pressure, though the temperatures are different. The admissi- 
bihty of the last assumption can be tested for any experiment 
by condensing and weighing the steam from each orifice sepa- 
rately. 

The radiation from this calorimeter may be formed by 
allowing the superheating steam to flow through the super- 
heater/, while the moist steam to be tested is shut off. The 
difference between the temperatures given by the thermometers 
at A and B under such circumstances is due to external radia- 
tion, and will be the same under like conditions ; let this loss 
be n degrees. Let the initial temperature of the superheat- 
ing steam be 4 ^^d the final temperature be t,, . Let the pres- 
sure of the steam be/, to which correspond the temperature t 
and latent heat r.^ Let the steam, which at first had the tem- 
perature / and contained i—:v of moisture, leave the orifice M 
with the temperature /^ . The heat yielded by the superheating 
steam is 0.48(4 — /^), of which 0.48/2 is lost by external radia- 
tion. The heat gained by the steam under test is (i ~ :i:)r 
+ o.48(/,-/). 

Consequently, 

0.48(4 -t,-n) = {i- x)r + 0.48(4 -t) ; 
^.^^_^^o.48[4-4-.-(4-/)]^ (^3^) 



Example. — The following are the data of a test made with 
this calorimeter in the laboratory of the Institute of Tech- 
nology : 

Pressure of the atmosphere, 14.7 pounds ; 

Gauge-pressure of steam, 71.7 " 

Final temperature of steam to be tested, . . . 33i°.8 F. 

Initial temperature of superheating steam, . . 417°. 4 F. 

Final '' '' " " . . 347°.4 F. 

Loss of temperature by radiation, ii°.7F. 



TESTING STEAM-ENGINES. 



^Z7 



o.48[4i7-4 - 347-4 - 1 1./ - (331-8 - 317.2)] 



891.7 



X = 0.024. 



It was found, by special experiment under the conditions of 
the experiment, that the radiation of the pipe leading to the 
calorimeter increased the moisture in the steam 1.2 per cent; 
consequently the priming is 1.2 per cent. 

Throttling Calorimeter. — A simple form of calorimeter, 
shown by Fig. 56, was devised by the author, which depends 
on the property that dry steam is 
superheated by throttling. Steam 
to be tested is brought in by a 
wrapped pipe a, below which the pt 
extension c with a drip at the end 
serves as a pocket to catch the 
water which may gather on the 
sides of the pipe. The valve at 3 
is opened a slight amount to admit 
steam to the chamber A, and the 
exit valve at d is used to regulate 
the pressure in the chamber. The 
temperature in the chamber is 
taken by a thermometer in a long 
cup at e, and the pressure is taken 
by the gauge /. Let the boiler- 
pressure be /, and let r and q be 
the latent heat and heat of the liquid corresponding. Let/, 
be the pressure in the calorimeter, and A^ and /, the total heat 
and the temperature of saturated steam at that pressure, while 
/j is the temperature of the superheated steam in the calorim- 
eter. Then 




Fig. 56. 



xr + g=^, + c^(^. 



r 



(285) 



238 



THERMODYNAMICS OF THE STEAM-ENGINE. 



Example. — The following are the data of a test made with 
this calorimeter : 

Pressure of the atmosphere, 14.8 pounds ; 

Steam-pressure by gauge, 69.8 " 

Pressure in the calorimeter, gauge, . . 12.0 *' 

Temperature in the calorimeter : . . . 268°. 2 F. 



X = 



1 1 56.4 + 0.48(268.2 — 243.9) — 286.3 
8^27 

Per cent of priming, 1.2. 



0.988 



A little consideration shows that this type of calorimeter 
can be used only when the priming is not excessive ; otherwise 
the wire-drawing will fail to superheat the steam, and in such 
case nothing can be told about the condition of the steam 
either before or after wire-drawing. To find this limit for any 
pressure, t, may be made equal to /^ in equation (285) ; that is, 
we may assume that the steam is just dry and saturated at that 
limit in the calorimeter. Ordinarily the lowest convenient 
pressure in the calorimeter is the pressure of the atmosphere, or 
14.7 pounds to the square inch. The table following has been 
calculated for several pressures in the manner indicated. It 
shows that the limit is higher for higher pressures, but that 
the calorimeter can be applied only where the priming is mod- 
erate. 

LIMITS OF THE THROTTLING CALORIMETER. 



Pressure. 








Priming. 






Absolute. 


Gauge, 




300 


285.3 


0.077 


250 


235 


3 


0.070 


200 


185 


3 


0.061 


175 


160 


3 


0.058 


150 


135 


3 


0.052 


125 


IIO 


3 


0.046 


100 


85 


3 


0.040 


75 


60 


3 


0.032 


50 


35 


3 


0.023 



TESTIXG STEAM-ENGINES. 239 

When this calorimeter is used to test steam supplied to a 
condensing engine, the limit may be extended by connecting 
the exhaust to the condenser. For example, the limit at 100 
pounds absolute, with 3 pounds absolute in the calorimeter, is 
0.064, instead of 0.046 with atmospheric pressure in the calo- 
rimeter. 

In case the calorimeter is used near its limit, — that is, when 
the superheating is a few degrees only, — it is essential that the 
thermometer should be entirely reliable, otherwise it might hap- 
pen that the thermometer would show superheating when the 
steam in the calorimeter was saturated or moist. In any other 
case a considerable error in the temperature will produce an 
inconsiderable effect on the result. Thus, at 100 pounds abso- 
lute with atmospheric pressure in the calorimeter, 10° F. of 
superheating indicates 0.035 priming, and 15° F. indicates 0.032 
priming. So also a slight error in the gauge-reading has little 
effect. Suppose the reading to be apparently 100.5 pounds 
absolute instead of 100, then with 10° of superheating the 
priming appears to be 0.033 instead of 0.032. 

Efficiency of a Steam-engine. — When the performance 
of an engine is given in pounds of water per horse-power per 
hour it is necessary to know also the pressure and quality of 
the steam used, and also to know the temperature of saturated 
steam at the pressure against which the engine exhausts. The 
difference of economy to be expected from high-pressure or 
low-pressure steam, from superheated or wet steam, or from a 
condensing or non-condensing engine, are specific instances of 
causes modifying the performance of an engine. 

There appears to be no good reason why the performance 
of an engine should not be stated in thermal units per horse- 
power per hour, which would enable us to compare directly 
all forms of engines without allowances or reductions. Such a 
method also leads at once to the consideration of the true 
efficiency of an engine. 

Suppose that an engine is supplied with M pounds of 
steam per stroke, having the pressure / and the quality x. 



240 THERMODYNAMICS OF THE STEAM-ENGINE. 

Then the heat in that steam above the heat in the same weight 
of water at freezing; is 



•fc) 



M{xr + q). 

Should the steam be superheated and have the temperature t^y 
then the heat in the steam is 

M{_c,{t,-t)^X\. 

Let the pressure against which the engine exhausts be /„ , at 
which steam has the temperature /„ and the heat of the Hquid 
q^. If the engine is a condensing engine the water in the hot- 
well, from whence the boiler is fed, can have nearly this tem- 
perature, and if the engine is non-condensing, then the feed- 
water can be raised nearly to this temperature by an exhaust- 
steam feed-water heater. It may be considered that the heat 
furnished to the engine per stroke is, for moist steam, 

M(xr-\-q-qX 

and that amount of heat must in general be given to the water 
and steam in the boiler by the fire. 

The work done by the steam per stroke, shown by the in- 
dicator, is W, the heat equivalent is A W. The efficiency of 
the engine is consequently 

'^' = M(7r'T~^) (^86) 

When d, the consumption of steam per indicated horse- 
power per hour, is stated, the efficiency is 

60 X 33000 X A , ^ . 

' Clxr + q-q^) ^ 

The last two equations give the efficiency of the fluid. The 
efficiency of the engine, determined by aid of a brake or dyna- 



TESTIXG STEAM-ENGINES. 24 1 

mometer, is found by substituting for (7,-, Cn the consumption 
of steam per net or brake horse-power per hour, so that 

• 6oX3300OX^ (,88) 

Similar equations may be deduced for superheated steam. 
The two efficiencies r}i and rfi, are to be compared with the 
maximum efficiency 



7; = 



T 



of a heat-engine working between the temperatures T'and T^, 
the absolute temperatures of saturated steam at the pressures 
/ and/„. 

Efficiency of the Boiler. — If the total heat of combustion 
of the fuel is H thermal units per pound, and if one pound of 
fuel evaporates in pounds of water from the temperature t^y 
which may or may not be equal to t^, to form steam having 
the quality x, at the pressure/, then the efficiency of the fur- 
nace and boiler is 

., = "<^--y-^-) . ..... (389) 

Efficiency of Engine and Boiler. — The efficiency of the 
engine and boiler combined is the product of the efficiencies 
of each separately ; that is, 

Vo = VnVb- 

Cost of Power. — The evaporative efficiency of a boiler is 
commonly given in pounds of water evaporated from and at 
212° F., equivalent to 965.8 B. T. U. per pound ; so that if m Is 
the actual evaporation as used above, and m^ the reduced evap- 
oration, 

^°- 965.8 ^"^^ 

16 



242 THERMODYNAMICS OF THE STEAM-ENGINE. 

Here also it would very much simplify matters if thermal 
units were used ; and then, without reduction, the evaporative 
efficiency could be given in thermal units per pound of fuel, 
which could be compared directly with the total heat of com- 
bustion. 

If the consumption of steam per net horse-power per hour 
is C,i pounds, so that the consumption of heat per horse-power 
per hour is 

Cnixr -\-q- q,\ 
then the consumption of coal per horse-power per hour is 

Cn{^r -\-q - q,) C^xr -\- q — q^ 



m{xr -\- q — q^ 7n^ 



(291) 



Efficiency Test. — The difficulty of arranging for the com- 
plete testing of large engines that are in continuous use has 
led to the proposal of a simple method by which the efficiency 
given by equation (286) may be found. The engine is indi- 
cated to determine A W, the work of the steam per stroke, and 
the condensing water and condensed steam delivered by the 
air-pump per stroke of the engine, from the jet condenser, 
flows in a well-mixed stream over a weir. If G is the injection- 
water per stroke, and M the steam used per stroke, then this 
gives 

M -\- G ^ numerical quantity. . . . (292) 

The initial and final temperatures /„ and 4 of the injection- 
water are taken by the aid of thermometers. 
Of the heat 

M{xr + q-q,) 

consumed by an engine per stroke, a part, A W, is changed 
into work, a part, Q,, is lost by external radiation, and the re- 
mainder, G{qk — q^, is carried away by the injection-water, so 
that 

M{xr + q-q,) = AW-\-Q,+ G{q,-q:). . (293) 



TESTING STEAM-ENGINES, 243 

In equation (293), W, q^ , and q^ are determined directly, r 
and q are known from the steam-pressure, and x may be deter- 
mined by calorimetric experiment, or may be known approxi- 
mately from previous experiments under like conditions ; also, 
Q^ may be known or determined. Under good conditions x is 
unity or differs but little from unity, and Q^ is small, so that it 
may be neglected without serious error. We have then, for an 
approximate result, two equations (292) and (293) with two un- 
known quantities, and may solve for M directly, and therefrom 
estimate the steam per horse-power per hour, or by equation 
(286) may find the efficiency. 

The chief advantage of this method is that it need not in- 
terfere with the ordinary running of the engine tested, and 
does not require much time or trouble. 



CHAPTER XV. • 

TESTS OF SIMPLE STEAM-ENGINES. 

In this chapter and the three following chapters will be 
given the data and results of several series of steam-engine 
tests, which were made to determine the relative economy 
of different methods of running engines and of different types 
of engines. 

Tests on the Michigan. — In 1861 experiments were made 
on the engines of the United States paddle-wheel steamer 
Michigan, at Erie, Pa., by a board of naval engineers, and re- 
ported by Isherwood,^ to determine the advantageous point 
of cut-off for naval engines of that type. 

This vessel had a pair of inclined direct-acting engines, with 
a jet condenser, and with the form of poppet-valves commonly 
used on American steamboats, but with the Sickles cut-off 
gear, by which the cut-off could be varied from the commence- 
ment of the stroke to ^ of the stroke ; and further, the cut-off 
could be varied from -j-^ to \^ of the stroke when the special 
cut-off gear was disconnected. 

The steam-pipe and cylinder sides were covered with felt 
and lagged with wood ; the cylinder-heads were uncovered ; 
the steam-pipes were so inclined that they drained into the 
cylinders. The main dimensions of the engines were : 

Diameter of cylinder, 36 in. 

Diameter of piston-rod, 3i in. 

Stroke of piston, 8 ft. 

Piston displacement, allowing for piston-rod, 56.544 cu. ft. 

Clearance, 3.280 cu. ft. 

Net area of steam-valves, 1 14.96 sq. in. 

Net area of exhaust-valves, 108.38 sq. in. 

* Experimental Researches in Steam Engineering. 

244 



TESTS OF SIMPLE STEAM-ENGINES. 245 

Diameter of paddle-wheel, 21 J- ft. 

Number of paddles, 16 

Width of paddles, 31 in. 

Length of paddles, 14 ft. 

There were two rectangular internally fired boilers, with 
vertical water tubes, each boiler having three furnaces. The 
boilers were of the type known as Martin boilers, which were 
much used in the navy. 

Manner of making Experiments. — The number of revo- 
lutions was recorded by a counter actuated by the engine. 
The feed-water was measured in a zinc-lined tank that held 70 
cubic feet. It was filled from the hot-well through a hose by 
the bilge-pump ; and there was a small hand-pump that was 
used to bring the level to the reference-mark each time with 
water from outside the vessel. The water was drawn from the 
tank by a feed-pump and distributed to the boilers. All con- 
nections to the boiler were broken and stopped with iron 
plates, and the hose from the bilge- and hand-pumps were 
thrown out of the tank after it was filled. The tank was 
pumped dry each time, and the feed-pipe emptied. The tem- 
perature in the tank was noted when it was half full. 

The coal was weighed on scales in equal portions. Refuse 
was weighed dry on the same scales and in the same manner. 

The steam-pressures were measured by a spring-gauge and 
a siphon mercurial gauge, the indications of which coincided. 
The vacuum was measured with a similar gauge. The atmos- 
pheric pressure was measured by an aneroid barometer, and 
the temperature was taken from a thermometer attached 
thereto. Two indicators were attached permanently to the 
two ends of the cylinder, and were actuated from the air- 
pump cross-head by a reducing lever. 

The temperature of the injection-water was taken by a ther- 
mometer on the side of the vessel opposite the hot-well discharge. 
The temperature of the hot-well was taken by a thermometer 
immersed in it. The temperature of the external air was taken 
on deck. 



246 THERMODYNAMICS OF THE STEAM-ENGINE, 

The boilers were fitted with gauge-cocks and glass water- 
gauges. The only outlet from the boilers was through the 
blow-off valve ; and any leakage would have to pass also a 
stop- cock and a Kingston valve. 

The vessel was secured to the dock, and was housed in, and 
the power of the engine was expended in paddling the water 
aft. Each experiment lasted 72 hours, during which the con- 
dition of working was not changed in any way. In anticipa- 
tion of the experiment, the engine was run several hours to 
bring it to the normal working condition. When all was ready, 
with average fires and proper steam-pressure and level of water 
in the glass gauges, the experiment was begun. During the 
experiment the working of the engine was made as regular as 
possible, and at the end of the 72 hours all conditions were left 
as at the beginning. The fires were cleaned at beginning 
and end ; and it was thought that the error from this source 
for a run of such a length was small. The steam-pressure 
varied not more than half a pound during the entire experi- 
ment. 

Indicator-diagrams were taken every half-hour, and each 
diagram measured separately. During all the experiments the 
throttle-valve was wide open, and the boiler-pressure was varied 
so as to keep the initial pressure in the cylinder constant. 

At the end of the experiments the paddles were removed 
from the wheel, and the mean pressure then required to move 
the engine was used in allowing for the friction of the engine 
and calculating the net power. 

The tightness and freedom from leakage of piston, valves, 
and stuffing-boxes was determined several times. 

The temperature of the gases in the up-take was noted by 
a high-grade mercurial thermometer, and was about 520° F. 

Three sets of observers with regular duties were arranged 
in watches, each superintended by a chief engineer of the navy. 

The data and results of the experiments are given in 
Table I. The table will be understood from the headings 
with very little added explanation. In order to make the re- 
sults of the different experiments directly comparable, the 



TESTS OF SIMPLE STEAM-ENGINES. 



247 



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34.797 
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rHOIOO-tlOOl- 



248 THERMODYNAMICS OF THE STEAM-ENGINE. 

mean effective pressure and the net effective pressures are given 
in a modified form, with the assumption of a uniform back pres- 
sure of 2.7 pounds, and of a pressure to move the engine un- 
loaded of 2.1 pounds. The modified horse-power and consump- 
tion per horse-power per hour are calculated on the same basis 
from the modified pressures. 

Discussion of Results. — All the experiments were made 
on the starboard engine, the other one being disconnected. 

In all the experiments the initial pressure in the cylinder 
was maintained constant, and the boiler-pressure was varied 
slightly for that purpose, but not enough to affect the results 
materially. The speed of the engine could not be controlled 
at the same time, but the variation from 11 to 20 revolutions 
could not interfere with the comparability of the results. 

The per cent of water in the cyHnder at the end of the 
stroke is not excessive for a cut-off at |-J- of the stroke. It in- 
creases rapidly to the cut-off at \y then it remained nearly con- 
stant to the cut-off at |-, and then increased again at a cut-off 
at ^y of the stroke. 

The consumption of steam per horse-power per hour is prop- 
erly a basis of comparison in these tests, since the boiler-pres- 
sure did not vary greatly during the tests. Since the variation 
of the back pressure is due either to a variation in the vacuum 
or to defects in the valve-gear or steam passages, and since an 
engine designed for a given expansion may be supposed to 
have adequate provision for maintaining a good vacuum, and 
for realizing it in the cylinder, it appears proper to compare the 
steam consumption corrected for variation of back pressure, 
and called the modified steam per horse-power per hour in the 
tables. 

The minimum consumption of steam per indicated horse- 
power per hour was found with a cut-off at f of the stroke, 
but it appears that the consumption is nearly the same for all 
points of cut-off from \ to y\ of the stroke. 

Comparing the consumptions per net horse-power per hour, 
the minimum is also at \ of the stroke in the table, but as the 
consumption for shorter cut-off increases rapidly and as no ex- 



TESTS OF SIMPLE STEAM-ENGINES. 249 

periments were made with the cut-off intermediate between f 
and -j^ , the most advantageous point of cut-off may be longer 
than -^- of the stroke ; and this seems not improbable, since the 
consumption with the cut-off at -^-^ of the stroke exceeds the 
consumption when the cut-off is at |- of the stroke by 2 per 
cent only. 

Considering the relative sizes of cylinders for the develop- 
ment of the same power, Isherwood concludes that for naval 
engines of this type and using saturated steam at a pressure of 
20 pounds above the atmosphere, it is advisable to use a cut- 
off at -j^ of the stroke, more especially as a special cut-off gear 
is not required in such case. 

Later experiments on engines using higher pressure of 
steam show that the advantageous point of cut-off becomes 
shorter and the number of advisable expansions becomes 
greater as the pressure increases. 

It is instructive to notice that the per cent of water in the 
cylinder at the end of the stroke increases as the cut-off is 
shortened, and that with the exception of Experiment 5, 
which for some reason has a greater consumption of steam 
than either the test preceding or following, the increase is 
quite regular. It appears that the condensation and re-evapo- 
ration and the exhaust waste in this type of engine, with low- 
pressure steam, very quickly counteract the gain to be antici- 
pated from expansion. 

Tests on the Mackinaw. — The tests on the engine of the 
United States steamer Mackinaw were made by a board of 
naval engineers* to determine the advantage of using super- 
heated instead of saturated steam, and at the same time an in- 
vestigation was made to determine the best point of cut-off. 
The Mackinaw was one of a number of paddle-wheel steamers 
built for special service during the years 1863 and 1864. It 
had one direct-acting inclined engine, with poppet-valves and a 
Stevens' cut-off. The engine was furnished with a surface con- 
denser. Steam was supplied by two Martin water-tube boil- 

* Experimental Researches in Steam Engineering. 



250 THERMODYNAMICS OF THE STEAM-ENGINE. 

ers, each having five furnaces. The principal dimensions of 
the engine were : 

Diameter of cylinder, 4 ft. lo in. 

Stroke of piston, 8 ft. 9 in. 

Diameter of piston-rod, 6J in. 

Displacement of piston allowing for rod, . 159.5356 cu. ft. 

Clearance, 13-5254 cu. ft. 

Area for admission and exhaust of steam, 393 sq. in. 

Diameter of paddle-wheel, 26 ft. 

Number of paddles, 24 

Length of paddle, 9 ft. 

Width of paddle, I ft. 3 in. 

Total grate-area, 200 sq. ft. 

Total water-heating s'urface, 5036 sq. ft. 

Superheating surface in up-takes, . . . 171 sq. ft. 

The experiments were made with the boat secured to the 
dock in the same manner and with the same precautions as 
those on the MicJiigait, The first five were made with the 
water-level at the normal height, so that the steam was prob- 
ably saturated. The last two were made with the water from 
five to six inches below the upper ends of the vertical water- 
tubes, so that the steam was superheated. 

The first five experiments were intended to be at the same 
speed of revolution of the paddle-wheels, but the number of 
revolutions fell to 5.609 per minute when the cut-off was at 0.21 
of the stroke in Experiment E, and Experiment A was made 
with 5.551 revolutions for sake of comparison. 

The data and results are given in Table II, and after the 
discussion of previous work require no explanation beyond 
that given by the headings. 

Discussion of Results. — Isherwood, in reporting these 
experiments, recalculated the results of the tests B, C, D, and 
E, on the following assumptions : 

(i) That the initial pressure was 50 pounds absolute, and 
the pressure at cut-off was 47 pounds absolute. 



TESTS OF SIMPLE STEAM-ENGINES. 



251 






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252 THERMODYNAMICS OF THE STEAM-ENGINE. 

(2) That the back pressure was 2 pounds, and the pressure 
to overcome the friction of the engine was i\ pounds. 

(3) That the mean total pressure was the same per cent of 
the initial pressure as it was in the actual experiment. 

The results are given in the following table : 



B. 


C. 


D. 


E. 


0.70 


0.56 


0.38 


0.21 


1.38 


1.68 


2.33 


3-68 


13.748 


31.948 


31.621 


38.485 


1. 00 


1.05 


1.24 


1.59 



Cut-off, . 

Number of expansions, 

Consumption per net horse-power estimated, 
Ratio of cylinders for equal powers, . . . 

An inspection of this table, or of the results in Table II, in- 
dicates that the consumption of steam per horse-power per hour 
is least with the cut-off at 0.38 per cent of the stroke, but that 
the consumption is but little greater with the cut-off at 0.56 of 
the stroke. It consequently appears that the advisable cut-off is 
at half-stroke or a little later, the difference between the results 
of this series of tests and the results of the tests on the Michi- 
gan being attributable to the difference of steam-pressure. 

The last two tests were made with superheated steam, ob- 
tained by running with the water-level in the Martin vertical 
water-tube boilers below the tops of the tubes, so that of the 
4036 square feet of heating surface about 1000 square feet were 
available for superheating. 

In these experiments the number of revolutions per minute 
was increased by removing a part of the paddles. In Experi- 
ment F the steam was strongly throttled, but in Experiment G 
the throttle-valve was wide open. 

If it be admitted that Experiments F and B may be com- 
pared, then the gain in consumption of steam per indicated 
horse-power per hour is 

32.913-24.59 ^^^ 
32.913 
A like comparison of Experiments E and G shows a gain of 

36.044 — 22.725 



36.044 
by the use of superheated steam. 



= 0.37 



TESTS OF SIMPLE STEAM-ENGINES. 253 

Tt is to be remembered that the apparent gain from super- 
heating is obtained while the engine is running nearly three 
times as fast, and exerting nearly three times the power that it 
did when using moist steam. 

Tests on the Eutaw. — The steamer Eutaw was one of the. 
same class as the Mackinaw, and differed only in that the cylin- 
der had two piston-rods instead of one, and that the boiler was 
furnished with a tubular superheater in the up-take, so arranged 
that the engineer could use saturated steam, superheated steam, 
or a mixture of saturated and superheated steam ; more prop- 
erly, the mixing of the two kinds of steam gave a ready method 
of controlling the degree of superheating. The piston displace- 
ment was 159.2258 cubic feet, but the clearance was the same 
as for the Mackinazv. 

The heating surface of the Martin boilers was so efficient 
that the products of combustion in the up-take were only 40 
to 80 degrees above the temperature due to the saturated 
steam in the boilers, so that to make a provision for superheat- 
ing the steam efficiently almost all of the water-tubes were 
removed from one furnace, and the tubular superheater was 
placed in the space thus provided. 

The experiments were made at Washington by a board of 
naval engineers,* with the vessel secured to the dock. It was 
intended that the steam-pressure should be the same through- 
out, and that the wheels should make the number of revolu- 
tions per minute that the power would give. 

Each experiment lasted 72 hours, and was made with the 
usual care and precautions required to give reliable results. It 
is believed that there was no leakage from the boiler nor in 
the cylinder, and that there was no priming. 

With natural draught on the superheater, the temperature 
of the superheated steam, as in F and G, was about 360 de- 
grees, while the temperature of the saturated steam was 270 
degrees, giving 90 degrees of superheating. When the blower 
was applied to the furnace connected with the superheater the 
temperature was (H, I, and J) about 390 degrees, showing 

* Experimental Researches in Steam Engineering. 



254 



THERMODYNAMICS OF THE STEAM-ENGINE. 





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TESTS OF SIMPLE STEAM-ENGINES. 255 

about 120 degrees of superheating. The highest degree of 
superheating did not appear to injure the metal of the cyhn- 
der. 

Discussion of Results. — At the time when these experi- 
ments were made, certain steamers plying on the Chesapeake 
Bay had superheating apparatus, and used strongly super- 
heated steam mixed with moist steam. It was claimed that 
a great economy was realized from the use of such mixed 
steam. In reality the whole apparatus was only a means of 
using superheated steam of which the degree of superheating 
could be controlled, and a comparison of the consumption of 
superheated steam per horse-power per hour for Experiments 
F to J with the consumption for Experiments K to O indi- 
cates that the differences, which are sometimes on one side 
and sometimes on the other, are due to the differing degrees 
of superheating and to the different initial pressures ; further- 
more, the differences are all small, and in many cases are within 
the probable error of the experiments. 

The smallest consumption of saturated or moist steam per 
horse-power per hour was obtained in Experiment B, with a 
cut-ofT at 0.32 of the stroke; but the consumption at 0.50 of 
the stroke being but little larger, it may be concluded as in 
the discussion of the tests on the Mackinaw that the cut-off 
may be chosen at about half-stroke. 

The smallest consumption of superheated steam per horse- 
power per hour appears to have been obtained with the cut-off 
at 0.50 of the stroke, but the varying degree of superheating 
prevents any conclusion on this point. Now the initial con- 
densation of moist steam interferes with the gain to be antici- 
pated from large expansion, and since superheated steam re- 
duces the initial condensation, it might be expected that its 
use would permit the use of higher degrees of expansion. No 
experiments can be quoted that are conclusive on this point. 

The consumption of moist steam for Experiment D is much 
greater than that for either Experiment C or Experiment E, 
and it is noticeable that the back pressure is much greater 
while the horse-power is less. No explanation is given by Ish- 



256 THERMODYNAMICS OF THE STEAM-ENGINE. 

erwood of these facts, though he includes this test with others 
in his comparisons, in which, however, he makes allowance for 
differences of initial pressure and back pressure. If we omit 
this experiment, the consumption of moist steam per horse^ 
power per hour with the cut-off at half-stroke was 32.7 pounds. 
The mean consumption of superheated steam for Experiments 
G, I, L, and N was 26.2 pounds. The gain from the use of 
superheated steam was therefore 

32.7 — 26.2 

— 0.20 nearly. 

32.7 ^ 

Taking the consumption of fuel per horse-power per hour 
as the basis of comparison, the real gain was 

2.87 — 2.40 

Dixwell's Tests. — The Harris-Corliss engine, now in the 
laboratory of the Institute of Technology, was fitted up by 
Mr. George B. Dixwell * for the purpose of making experi- 
ments on superheated steam. At his request a board of three 
engineers of the United States Navy witnessed a series of ex- 
periments made on this engine in 1877 with apparatus belong- 
ing to the Institute. 

The following is the substance of the report made by the 
board, of which C. H. Loring, Chief Engineer U. S. N., was 
the senior officer : 

In the apparatus employed steam was taken from the hori- 
zontal tubular boilers which supplied steam for heating the 
buildings of the Institute of Technology, and for other pur- 
poses. 

The engine is of a well-known Corliss type, of 8 inches diam- 
eter and 24 inches stroke of piston. The cut-off was varied by 
an Allen governor. The entire clearance is -^\-^ of the space- 
displacement of the piston. 

* Proceedings of the Society of Arts, M. I. T. 1887-88. 



TESTS OF SIMPLE STEAM-ENGINES. 257 

The power developed by the engine was absorbed by a fric- 
tion-brake applied to the fly-wheel. 

The exhaust steam from the engine passed to the calorim- 
eter, which comprised the following details : 

I. A tank built of planks two inches thick, of about 120 
cubic feet capacity, containing a system of tubular metallic con- 
densing surfaces, the interior of the latter being in communica- 
tion with the exhaust-pipe of the engine and with the receiving- 
tanks hereinafter described. The body of the tank could be 
filled with water from the city aqueduct, by which heat in the 
steam discharged from the cylinder into the system of condens- 
ing tubes was absorbed. To relieve the walls of the tank from 
pressure resulting from the expansion of the water in heating, 
a small vessel of ten feet cubical capacity, two feet high, of 
w^ood, was placed above the large tank described above, com- 
municating with the latter by a pipe of two inches diameter. 
Through this pipe the expanding water could rise to the upper 
vessel described, which is called the expansion tank. The es- 
cape of vapor was prevented by a floating cover in the expan- 
sion tank, joined to the walls by a flexible diaphragm. The 
large tank, the expansion tank, and their contents and appen- 
dages, stood upon the platform of a Fairbanks scales. Free- 
dom of movement, within sufficiently wide limits, was main- 
tained by fitting the pipe connections of the tank with rubber 
tubing ; and the weighing was accurate within two pounds ; the 
whole weight, tanks, appurtenances, and water being 8100 
pounds. 

The tank was fitted with thermometers for ascertaining the 
temperature of the hydrant water entering, and of the water 
contained. To insure equality of the latter quantity in all 
parts of the tank chamber, a device for circulating the water 
was provided, to be worked by hand. 

The fall of pressure in the condenser tubes, below that of 
the atmosphere, was averted by the automatic action of a re- 
verse, or vacuum, valve. 

2. The pipe leading from the lower end of the condensing 
tubes, through which the water resulting from condensation 



258 THERMODYNAMICS OF THE STEAM-ENGINE. 

passed out of the large tank, entered a small tank, which, like 
the others, was made of 2-inch plank. This tank stood upon 
the platform of a second Fairbanks scales, and was fitted with 
a thermometer for ascertaining the temperature of its contents. 
This tank could be emptied through a pipe leading to the 
sewer. The pipe connections were, like those of the large 
tank, flexible, so as to admit of weighing. 

The superheating apparatus consisted of a cylindrical 
boiler, of iron, seven feet long and three feet in diameter, fitted 
with fifty iron tubes two inches in diameter and five feet long. 
The latter were fire tubes, vertical, and six inches of the lower 
end covered with water. The superheater was set in brick- 
work, in which an annular space allowed the products of com- 
bustion to pass downward, around a part of the shell. The 
furnace was of brickwork, so far removed from the heating 
surfaces as to prevent direct radiation to them from the fuel. 
In this vessel the steam from the boiler could be superheated 
above 600° F. 

The superheated steam was delivered to the engine through 
a 2^-inch pipe. At the receiving end of this pipe a pipe of if 
inches diameter delivered saturated steam, the admission being 
regulated so as to govern the temperature of the steam passing 
through the pipe, which nevertheless remained superheated to 
a degree measured by a Bulkley pyrometer, placed five or six 
feet beyond. 

A mercurial thermometer was placed close to the steam- 
chest of the engine, in the steam-pipe, and another Bulkley 
pyrometer in the clearance space of the cylinder. A mercu- 
rial thermometer was also placed at the point last mentioned. 
During a part of the experiments, a mercurial high-grade ther- 
mometer was placed nearly midway of the length of the steam- 
pipe. 

Besides the pipes described, others connecting the engine 
directly with the generator were fitted. These were cut off 
from the former at will, by gate-valves made perfectly tight- 

An indicator was fitted to each end of the cylinder. 



TESTS OF SIMPLE STEAM-ENGINES. 259 

The experiments were made in pairs, as follows : 

1. Saturated steam, ^ cut-off; followed by one at the same 
cut-off with superheating. 

2. Saturated steam, -^-^ cut-off ; followed by one at the same 
cut-off with superheating. 

3. Saturated steam, -J- cut-off ; followed by one at the same 
cut-off with superheating. 

Diagrams from each end of the cylinder were taken, and 
readings from the pressure-gauge and thermometers, and of the 
weighing scales, were registered every five minutes. The large 
tank was heated, before the beginning of each experiment, to 
the temperature at which it was desired to close the experi- 
ment ; then emptied, and weighed empty ; then filled with 
water from the city aqueduct, at the natural temperature, the 
temperature observed, and the full tank weighed. Throughout 
each experiment the water in the tank was kept in motion, that 
the circulation might prevent differences in temperature within 
it. The temperature and weight of the tank water at the end 
of the experiment was registered after clearing the condensing- 
tubes of water. The water delivered into the small receiving- 
tank was also weighed, and its temperature ascertained every 
five minutes. From these quantities the total heat of the steam 
leaving the cylinder is computed. 

It was sought to maintain in the cyHnder, during each ex- 
periment with superheated steam, a temperature 310° F., and 
an initial pressure of 50 pounds by the gauge. 

It will be seen from Table IV, page 261, which contains the 
averages of all the observations recorded, that this was very 
nearly accomplished. 

It will also be seen that to maintain the above temperature 
within the cylinder a varied degree of superheating was neces- 
sary, accordingly as the cut-off was varied. 

After the experiments were completed, the correctness of 
the instruments used was verified by the very accurate methods 
of the Institute of Technology. It was then ascertained that 
some leakage of piston and valves had existed. This leakage 
affects the cost of the power, but not the correctness of the de- 



26o THERMODYNAMICS OF THE STEAM-ENGINE. 

ductlons from the data obtained, in their bearings upon the 
object of the experiments. 

Discussion of Results. — The following points are notice- 
able features of the experiments, and of the action of the ap- 
paratus: 

1. Throughout all the experiments with saturated steam, 
considerable variations in the temperature of the cylinder were 
indicated by the thermometer and the pyrometer during every 
stroke of the piston. The amplitude of the vibrations of the 
pyrometer extended over nineteen degree-marks of the dial. 
But throughout the whole of every stroke of the piston, during 
the experiments with superheated steam, these instruments 
constantly indicated a fixed degree of temperature, showing no 
vibrations whatever. 

At the close of the half-stroke and the seven-tenths stroke 
cut-ofT experiments with superheated steam, the same instru- 
ments showing no vibrations, the cut-off was shortened without 
change in the superheating. Vibrations of considerable ampli- 
tude were presently observed in them. 

2. The remarkable fall of temperature of the steam in pass- 
ing from the superheater to the steam-chest, before entering 
the latter, being for J cut-off, 97°; for |- cut-off, 49°; for ^, 

3. During experiments with superheated steam the open- 
ing of the indicators for preliminary heating was attended by a 
sudden fall of 15° F. within the cylinder, the temperature gradu- 
ally rising again as the metal of the indicators became heated. 

After using superheated steam, five minutes were required 
for a fall of 15°, the steam being shut off. 

The least consumption of steam, whether moist or super- 
heated, was found with the cut-off at 0.44 of the stroke. The 
gain in steam consumption from the use of superheated steam, 
with about 140° F., superheating, was 
42.2 - 31.7 



42.2 



0.25 nearly; 



but since fuel was used to superheat the steam the real gain 
was not so great. The fuel consumption could not be deter- 



TESTS OF SIMPLE STEAM-ENGINES. 



261 





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262 THERMODYNAMICS OF THE STEAM-ENGINE, 

mined in these tests, so the real gain may be estimated as fol- 
lows. The steam from the boiler probably contained one per 
cent of moisture, so that each pound of steam may be assumed 
to have brought to the cylinder of the engine 

0.99^ + ^ — ^o'== 0-99 X 901.9 + 272.5 — 183.9 = 981.5 B.T. U., 

in which r and q are the latent heat and heat of the liquid for 
the temperature of 303° F., and q^ is the heat of the liquid at 
15.65 pounds pressure. On the other hand, the superheated 
steam brought in per pound 

<^p{t^ — t)-\-'^ — q, = 0.48(441 — 299.4) + 1 173.2 — 182 

= 1059.2 B. T. U., 

in which Cp is the specific heat of superheated steam at constant 
pressure, and t, is the temperature of the superheated steam in 
the steam-pipe near the throttle-valve ; / is the temperature of 
saturated steam at the pressure in the steam-pipe, and \ is the 
total heat of steam at that temperature and pressure ; while q^ 
is the heat of the liquid at the pressure of the back pressure. 
There appears to be a discrepancy between the boiler-pressure 
and the initial indicated pressure in each experiment, so that 
the initial pressure in the cylinder has been taken in this calcu- 
lation. 

The number of thermal units per horse-power per hour fur- 
nished to the engine in the test with saturated steam was 

42.2 X 981.5 ==41420, 

while with superheated steam the number of thermal units was 

31.7 X 1059.2 = 3358, 

and the gain from the use of superheated steam was 

41420—33580 



41420 



— 0.19 



In the experiments made with saturated steam the per 
cent of water at cut-off decreased rapidly as the cut-off was 



TESTS OF SIMPLE STEAM-ENGINES. 263 

lengthened, and the per cent of water at release also decreased, 
though much less rapidly. 

In the experiments made with superheated steam. Experi- 
ment 5 shows the same per cent of water at cut-off and at re- 
lease, which indicates that the condensation and re-evaporation 
during expansion were equivalent. Experiment 4 shows re- 
evaporation during expansion, and Experiment 6 shows con- 
densation during expansion. 

By aid of the last column of Table IV the per cent of mois- 
ture in the exhaust steam may be calculated as follows : The 
mean back pressure is 15.35 pounds, at which the heat of vapo- 
rization is 964.4 and the heat of the liquid is 183, so that if x is 
the part of the mixture that is steam, 

964.4;^ -|- 183 == 1046 ; 

.-. X — 0.895, 

and the per cent of moisture is 10.5. 

The other experiments with saturated steam show a less 
degree of moisture. The experiments with superheated steam 
show that the exhaust steam was superheated in the two last 
experiments, and that it was moist in Experiment 4. 

Automatic Cut-off Engines. — At the First Millers' Inter- 
national Exhibition at Cincinnati, June 1880, som.e competi- 
tive tests were made by John W. Hill on three automatic cut- 
ofi'-engines, condensing and non-condensing, the results of 
which are of interest since they show the performance of well- 
made unjacketed simple engines. 

Two of the engines were modified forms of the well-known 
Corliss engine, known as the Reynolds-Corliss and the Harris- 
Corliss engines. The third engine made by Wheelock had 
two semi-rotative valves similar to the CorHss valve, one at 
each end of the cylinder to give admission and exhaust of 
steam, and also two cut-off valves of similar form, which cut off 
the supply of steam to the -main valve. It had consequently 
two clearances, one for compression, and a larger one, including 
the space between the two valves, for expansion. 

The dimensions of the engines were as follows : 



264 THERMODYNAMICS OF THE STEAM-ENGINE. 

DIMENSIONS OF ENGINES. 



Diameter of cylinder, inches 

" " piston-rod, inches 

" " steam-pipe, inches 

" " exhaust-pipe, inches 

" " fly-wheel, feet 

Area steam-ports, square inches 

Area exhaust-ports, " " 

Stroke of piston, inches 

Weight of engine, exclusive of fly-wheel, 
pounds 

Weight of fly-wheel, pounds 

Clearance in decimal of stroke 

Release in decimal of stroke, condensing.. 
" " " non-condensing. 

Exhaust closure in decimal of stroke, con- 
densing 

Exhaust closure in decimal of stroke, non- 
condensing 

Diameter air-pump cylinder, inches 

Diameter injection-pipe, inches 

Diameter overflow-pipe, inches. 

Stroke of air-pump piston, inches 



Reynolds- 
Corliss. 



18.02 
2.812 
S 
7 

16 

15-75 

27 



22,180 

[4,694 
0.0265 
0.978 
0.981 

0.056 

0.083 
17 



Harris- 
Corliss. 



16 

13-50 
24-75 
48 

18,000 

11,950 
0.0193 
0.940 
0.969 

0.122 

0.120 
9.81 



Wheelock. 



18.26 

2.9375 

7 

8 

16 
30 



9,000 
12,000 
0.0235 & 0.0142 
0.956 
0.970 

0.056 



0.084 

2 
3-5 



The Wheelock engine had a Bulkley condenser, with the 
head of the condenser set 34 or 35 feet above the level of the 
hot-well so that no air-pump was required. 

The feed-water supplied to the boilers furnishing steam for 
the tests was weighed in a tank on scales. The quality of the 
steam was determined by a continuous calorimeter. The con- 
densing water was measured by a water-meter, and though the 
quantities thus determined are introduced in the tables they 
cannot be taken with full confidence. 

The steam-pressure in the boiler and in the steam-pipe, and 
the vacuum in the condenser, were taken with gauges. The 
pressure of the atmosphere was taken with an aneroid ba- 
rometer. 

All temperatures were taken with mercurial thermometers. 

Diagrams were taken every fifteen minutes with Thomp- 
son indicators at each end of the cylinder, and all o.ther obser- 
vations were read at the same intervals. 

The work of the engines was applied to drive rotary 
pumps. Attempts were made to find the friction of the en- 
gines, and tests of regulation at various loads were also made. 

The summary of the results of tests are given in Table V : 



TESTS OF SIMPLE STEAM-ENGINES. 



265 



TABLE V. 

Automatic Cut-off Engine. 



Duration of trial hours 

Steam-pressure, boilers pounds 

" pipe " 

Barometer inches hg. 

Vacuum in condenser " " 

Temperature of air Fahr. 

" of injection " 

" of overflow " 

Revolutions per minute, engine 

" " air-pump 



Diagrams. 

Initial pressure pounds 

Cut-off in decimal of stroke 

Pressure at cut-off pounds 

Terminal pressure, absolute " 

Counter-pressure at mid-stroke " 

Maximum compressiorf pressure " 

Mean effective pressure " 

Loads. 

Indicated horse-power 

Friction of engine 

Extra friction due to load, estimated 

Power absorbed by air-pump 

Net effective horse-power 

Coefficient of useful effect 



Calorimeter. 

Condensing-water, per hour pounds 

Condensation-water, " " 

Temperature of injection Fahr. 

" " overflow " 

" " condensation " 

Thermal value of steam B. T. U. 

Relative value of steam 



Steam Expended. 

Water weighed to boilers 

Leakage of tanks 

" of pipe 

Correction for variation of water-level. 

Condensation in calorimeter 

Net steam delivered to engine 



Economy of Engine. 
Steam per indicated horse-power per hour, 

actual 

Steam per net horse-power per hour actual. 
Steam per indicated horse-power per hour 

corrected for relative value of steam 

Calculated Economy. 
Steam per horse-power per hour by the dia- 
grams. . 

Condensing Water. 
Water expended per hour 



Water expended per pound of steam . 



Condensing. 



Rey- 
nolds- 
Corliss. 



95.8 

92.5 
29.72 

25-45 
84°. 2 

72.4 
101.7 

75-4 

59-1 



91. 1 
0.124 

86.3 
15-2 
4-5 
13.6 
35-4 



162.3 
10.6 
6.1 

!&% 

0.879 



1427 
68 

77° 
131° 
107° 
1243 



34425 

26.25 

29 -5 
-142.8 
620.025 

33606 



23-5 
19-5 



103783 
30.9 



Harris- 
Corliss. 



96.1 

91.7 
29-55 
25.67 
87°. 6 
75-9 
97-5 
75-8 
75-8 



90.1 
0.119 



14.6 

3-4 

26.6 



165.6 
9.6 
6.2 

id.l 

0.876 



1405 7 
50-55 

78°. 07 
121°. 87 

97°. 86 

1315-9 
1. 000 



32296 
13- 

+285.7 
505 . 500 



19.4 



104307 
32-5 



Whee- 
lock. 



Rey- 
nolds- 
Corliss. 



0.131 

77-7 
14.0 
4-7 
28:1 
33-9 



158.4 

7.8 

6.0 

*o.6 

143.9 

0.909 



1797-5 
69.20 

77°. 24 
123°. 25 
106°. 57 
1301.7 
0.989 



31538 



692.000 
30847 



19.5 

21.4 



76324 
24.7 



Non -condensing. 



96.6 

92-5 
29-75 

87°-4 



34-7 
29.8 



137-0 
10.3 
5-1 

121.7 

0.88 



'in, 

76°. 86 


1530 

54 
77° 


9 

77 

87 


34° -86 
04° -45 


119° 
980 


% 


211. 3 


1255 


7 



32645 

20.5 
15-75 

615.000 
31994 



25.9 

29.2 



23-9 



19.0 



Harris- 
Corliss. 



91-5 
29-55 



89-S 
0.136 

85-9 
17.0 
0.4 
46.1 
28.9 



134-3 
9.6 
50 

119 7 



32708 



547-750 
32160 



23.9 

26.8 



Whee- 
lock. 



96 3 

91-5 
29.48 

78° '.8 



76. 



88.5 
0.170 

76.9 
17-5 
i.o 
44.2 
29.4 



140.0 
8.0 
5-3 

126.7 

0.905 

1836.3 
67.70 
76°. 45 
120°. 85 
108°. 74 
1313-1 



-214.3 

645-750 
34889 



24.9 

27-5 



19.8 



* Power required to raise water for condenser. 



2^^ THERMODYNAMICS OF THE STEAM-ENGINE. 

Hoadley Portable Engine. — The following are the data 
and results of a test on a Hoadley portable steam-engine, 
made at the International Exhibition, at Philadelphia, 1876. 
The engine was a simple single-cylinder engine, lagged but not 
jacketed, with a piston slide-valve controlled by an automatic 
governor, and mounted on the top of an unclothed locomo- 
tive boiler. The coal was anthracite of ordinary quality, used 
without drying. 

Test of a Hoadley Portable Engine. 

Diameter of cylinder, 14.56 in. 

" " piston-rod, 2.375 " 

Length of strolce, , . . . 1.66 ft. 

Clearance, fraction of piston displacement : crank end, . 0.077 

head end, . 0.157 

Duration of test, 6 hrs. 2 min. 

Revolutions per miaute, 125.96 

Steam-pressure in boiler, 120 lbs. 

Initial pressure : crank end, 124.75 

head end, ii9-9 

Absolute pressure at end of stroke : crank end, .... 23.4 

head end, .... 31.9 

Absolute pressure at admission : crank end, 112.5 

head end, ..... 117. 7 , 

Mean absolute forward pressure : crank end, 58.4 

head end, . ... 69.2 

Mean absolute back pressure : crank end, . . ... 24.7 

head end, ...... 25.9 

Mean effective pressure : crank end 33.7 

head end, 43.3 

Point of cut-off : crank end 0.1439 

head end, 0.2091 

Indicated horse-power : crank end 34.6 

head end, 45-69 

Total, 80.29 

Horse-power by brake, 72.72 

Friction of engine, horse-power, 7.57 

Horse-power by indicator without load, 5.80 

Steam per I. H. P. per hour, weighed, 25.61 lbs. 

" " brake H. P. per hour, weighed, 28.27 

" " I. H. P. per hour, indicator, 19-38 

" " brake H. P. per hour, indicator, 21.4 

Coal per indicated horse-power per hour, 3.35 

" " brake " <» «< 2. 69 



TESTS OF SIMPLE STEAM ENGINES. 26 J 

Heating surface of boiler, 461. 5 sq; ft. 

Area of grate, 12.75 " 

Coal per sq. ft. per hour, 21.07 lbs. 

Water evaporated per sq. ft. per hour, heating surface, . 4.46 " 

Ratio of ashes to coal burned, o. 118 

Water evaporated per pound of coal, 7.65 lbs. 

" combustible, 8.68 " 



CHAPTER XVI. 

TESTS OF SIMPLE AND COMPOUND ENGINES. 

The several series of tests following give the data for the 
comparison of the performance of simple and compound engines. 
All the tests except those on the Gham were made by engi- 
neers of the United States Navy and the United States Rev- 
enue Marine, and consist of tests on the coast-survxy steamer 
Bache ; of tests on the revenue steamers Rush, Dexter, and 
Dallas ; and of tests on the revenue steamer Gallatin ; also of 
tests on the Herreshoff steam-yachts Leila, Siesta, and on the 
yacht Gleam. 

The principal dimensions of the engines and boilers of the 
United States steamers are given in the following table : 

Dimensions of Engines and Boilers. 





Bache. 


Rush. 


Dexter. 


Dallas. 


Gallatin. 


Diameter of cylinders, ins., high pressure 
'• low 
" " piston-rods, ins., high " 


15-98 

25 
2-5 
3-625 

4-05 

I : 2.4398 

31-16 
950.10 
54-32 


24 
38 

27 

7.887 

5849 

1572.85 


26'"" 

36"" 
5-37 

1572.85 


■36"" 

30 
S.02 

57 
1689 24 




34-1 

30 

6.- 59 


Clearance, per cent, high pressure 

" low •' 


Grate surface SQuare feet . 


55 25 

1805.163 

105. 311 


Water-heating surface, square feet 

Steam-heating surface, " " 



Tests on the Bache. — The engine and hull of the United 
States coast-surv^ey steamer Bache were built in 1870 from 
designs by INIr. Emer}^,^ then consulting engineer to that de- 
partment. The engine is a direct-acting, inverted, compound 
engine, with the small c\-linder above the large cylinder, both 
pistons being attached to one piston-rod. The small cylinder 



Journal Franklin Institute, May, 1S75. 



263 



TESTS OF SIMPLE AND COMPOUND ENGINES. 269 

was not jacketed, but the large cylinder had a steam-jacket on 
the sides and ends ; when working compound the steam for 
the jacket was taken from the bottom of the small steam-chest ; 
when working as a simple engine, with the small cylinder dis- 
connected, the steam was taken from the main steam-pipe. 
Suitable pipes and valves were provided so that steam could be 
supplied directly to the large cylinder, and excluded from the 
small cylinder, in which case the large cylinder acted as a sim- 
ple expansive engine. Ordinarily the steam passed from the 
small to the large cylinder through a large pipe which acted as 
intermediate receiver. Both cylinders were provided with short 
slide-valves and independent cut-off valves on the back of the 
main valves, and the valves of both cylinders were actuated by 
continuous valve-stems. The engine had a surface condenser. 
The air-pump was operated by levers from the main cross-head. 
The circulating pump was of the centrifugal pattern, driven by 
an independent engine. 

During the trials the vessel was secured to the dock. 

The feed-water was measured in a tank with two compart- 
ments that were filled and emptied alternately. The capacity 
of each compartment was ascertained by weighing water into 
it, of the average temperature of the feed-water. Indicator- 
diagrams were taken every twenty minutes. 

The water-level in the boiler was noted every time the 
feed-water tank was filled, but it did not vary appreciably. 
The condensed water from the jackets and receiver was col- 
lected and weighed separately and returned to the feed-water 
tank. 

In the ninth experiment the coal was weighed, but in the 
others, which were shorter in duration the water only was 
weighed. The coal used was anthracite of fair quality. 

The data and results of the experiments are given in 
Table VI. 

Tests on the Rush, Dexter, and Dallas. — In 1874 three 
vessels were built for the United States Revenue Marine, 
which were designedly alike in all respects, except that the 
engines were of three distinct types, and the boilers were 



2/0 



THERMODYNAMICS OF THE STEAM-ENGINE. 



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TESTS OF SIMPLE AND COMPOUND ENGINES. 2/1 

adapted to the engines. The Ricsh had a direct-acting, in- 
verted, compound, receiver engine, with the cranks 90°, thor- 
oughly steam-jacketed, felted, and lagged, designed to use 
steam at 80 pounds pressure. The small cylinder had an inde- 
pendent cut-off valve on the back of the main valve ; the large 
cylinder had a double-ported valve arranged to cut off at about 
half-stroke. 

The Dexter had a single-cylinder, direct-acting, inverted en- 
gine, felted and lagged, but not steam-jacketed. The cut-off 
could be varied by adjustable cut-off plates on the back of the 
main valve. The steam-pressure was intended to be 70 
pounds. 

The engine of the Dallas was also a single-cylinder, in- 
verted engine, but was intended to carry a steam-pressure of 
40 pounds. The cylinder was covered with a non-conducting 
composition and lagged, but not steam-jacketed. Steam was 
distributed by a slide-valve with adjustable cut-off plates on the 
back. 

The experiments were made under the direction of Chief 
Engineer C. H. Loring, U. S. N., and Chas. E. Emery,* Con- 
sulting Engineer U. S. R. M., assisted by two chief-engineers 
of the navy and two of the revenue marine, with a sufficient 
force of assistants and helpers. 

During the experiments the vessels were secured to the 
dock. 

The coal, which was anthracite of fair quality, was sent 
from the dock in bags, filled to a certain weight, as wanted. 
The ashes were measured in buckets and then weighed in 
gross on the wharf. One experiment on each engine was of 
sufficient length to determine the evaporative efficiency with 
certainty. The other experiments were shorter, and for them 
the consumption of water only was determined. 

The feed-water was measured in a tank with two compart- 
ments, which were alternately filled and emptied, as it came 
from the condenser and passed to the boiler. The waste from 



* Journal Franklin Instituic, 1 av. 1875^ 



272 THERMODYNAMICS OF THE STEAM-ENGINE. 

leakage, etc., was supplied from a hydrant and charged in the 
cost. 

A number of indicators were compared under steam-pres- 
sure with a standard gauge, and a pair selected that were cor- 
rect at varying pressures. Diagrams were taken every twenty 
minutes. 

The data and results are given in Table VII. 

Tests on the Gallatin. — The United States revenue 
steamer Gallatin, built in 1870, was re-engined in 1874 accord- 
ing to designs of Mr. Charles E. Emery, and tested by Chas. 
H. Loring, U. S. N., and Mr. Emery* at the Boston Navy 
Yard in Dec. 1874 and Jan. 1875. 

The Gallatin had a single, inverted, steam-jacketed, direct- 
acting engine, with a slide-valve set to cut off at two-thirds 
stroke, and an adjustable cut-off valve on the back of the main 
valve. The air-pump was operated by levers from the main 
cross-head. The cooling water for the surface condenser was 
supplied by a centrifugal pump driven by an independent en- 
gine. The boiler, steam-pipes, and cylinder were covered 
with hair-felt and canvas, and in the engine-room the exposed 
parts were covered with Russia iron or wood lagging. 

Steam for the jackets was ordinarily conducted through a 
felted pipe from the bottom of the valve-chest to the upper 
part of the cavity in the cylinder cover. A second pipe leads 
from the bottom of the cavity in the cover, upward and around 
to the side jacket, which is in common with the jacket for the 
bottom of the cylinder. Thus any water which collects in the 
bottom of the valve-chest or cylinder cover is carried into the 
main jacket, from which all water is blown into the hot-well 
through an intermediate vessel provided with a glass gauge. 

The boiler was designed to carry a steam-pressure of 60 
pounds ; during the tests it was worked at 70 pounds part of 
the time, to compare with tests on the other engines. 

The experiments were made with the vessel secured to the 
wharf. 

* Report of trial. 



TESTS OF SIMPLE AND COMPOUND ENGINES. 



273 





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i-4^^r-l)H 



2/4 THERMODYNAMICS OF THE STEAM-ENGINE. 

The coal, which was anthracite of fair quaHty, was weighed 
in bags on the wharf and sent on board as needed. The ashes 
were hoisted in buckets and weighed in bulk on the wharf. 

The condensed steam from the surface condenser was 
measured in the tank with two partitions, which was used in 
the tests on the revenue steamers already described. The 
water from the jackets was cooled by passing it through a coil 
in a ship's distiller, and then weighed in an open tank. After 
the water was weighed it was delivered to the condenser, and 
thus was charged in determining the cost of power. 

The indicator-diagrams were taken every twenty minutes. 

To ascertain the evaporative efficiency of the boiler the 
machinery was operated continuously for 48 hours with the 
steam-pressure at 70 pounds. 

In all cases when the steam-jacket was not in use, a joint in 
the pipes was broken to let in air and to detect leakage of 
steam into the jackets. 

In working out the results some of the experiments dis- 
covered discrepancies, and when errors in observations were de- 
tected such experiments were rejected ; but when no errors 
were found the tests were reported with the others, though all 
such unsatisfactory tests were made in the first of the work, 
before the observers were familiar with the work. In the tests 
numbered 13, 30, 34, 37, 40, 41, and 42, distinguished by an 
asterisk in the table, some of the indicator-diagrams were faulty, 
and were corrected by comparison with diagrams taken under 
like circumstances. 

Discussion of Results. — From the data and results given 
in Tables VI, VII, and VIII may be found the advantage 
of the use of compound engines, of the use of steam-jackets, 
and of the use of high-pressure instead of low-pressure 
steam. 

In order to make the comparison more readily the follow- 
ing table is given, in which are collected «some of the data and 
results of those tests that gave the best efficiency under differ- 
ent conditions. 



TESTS OF SIMPLE AND COMPOUND ENGINES. 



275 



Simple and Compound Engines. 



Name of engine. 



Bache 

Rush 

Bache 

Dexter 

Gallatin 

Reynolds-Corliss 



Method of working. 



Compound with jacket 
without " 
" with " 

Simple with jacket 

•' without" 

" with " 

" without " . .. . 



2" So 



tn 3 

CQ 3 



3-3 
3-4 
3-5 
3-7 
4.4 
3-4 
4.0 

3-9 
4-5 



3 c 



53-2 
47-7 
70.8 
53-8 
47.1 
56.5 
61. 1 
59-9 
75-4 



H o 



4J O 



|li 

^-« i2 V- 
j_, o <u 



.0 


99. 


•7 


6q. 


.2 


266. 


.1 


116. 


■3 


8q. 


•■^ 


I8S 


.0 


306 


•9 


279 


.8 


162 



20.3 
23.0 

18.4 

23.2 
26.2 
23-9 
20.7 






21700 
24500 
19600 
24700 
27600 
25400 
21900 
23200 
21800 



In the group of tests on the Gallatin with the steam-jacket 
in use and with about 70 pounds boiler-pressure, there are 
three that have nearly the same consumption, and of these the 
one Avas chosen which had nearly the same number of expan- 
sions as the other tests in the above table, and with which it 
should be compared. The test on the Reynolds-Corliss engine 
was included in the same table, since it is instructive to com- 
pare it with the tests on marine engines. 

Direct comparison of the consumption of steam per horse- 
power per hour of the tests given in the table is liable to be 
misleading, on account of the difference in boiler-pressure and 
back pressure. The estimated number of thermal units per 
horse-power per hour has been calculated, on the assumption 
that the steam in the boiler is dry and saturated, by the ex- 
pression 

in which X is the total heat at the boiler-pressure and q^ is the 
heat of the liquid at the back pressure. The back pressure is 
chosen instead of the pressure in the condenser, since the effi- 
ciency of the fluid is to be considered rather than the efificiency 
of the engines. 

The least consumption of steam is shown by the engine of 
the Rush, working compound with both cylinders thoroughly 
steam-jacketed. This test may properly be compared with 
the test on the engine of the Gallatin, working single, and 



2^]^ 



THERMODYNAMICS OF THE STEAM-ENGINE. 



TABLE VIII. 
Tests on the Gallatin. 











Dura- 
tion, 
hours. 


Cut-off 
fraction 

of 
stroke. 


Ratio 
of 
ex- 
pan- 
sion. 


Temperatures, 
Fahrenheit. 




Description of Test. 


Ex- 
ter- 
nal 
air. 


En- 
gine- 
room. 


Sea- 
wat'r. 


1 

2 
3 
4 
5 
6 


\ Steam-jacket not in use -j 

>• Steam-jacket in use -j 

1 Steam-jacket supplied with steam at 70 j 
) pounds 1 


1. 9166 
2.25 
2. 1 

2.1333 
2.2166 
2.2 


0.463 
0.640 
0.468 
0.648 
0.525 
0.626 


2.02 

1-51 
2.00 

\t 

1-54 


3^ 

38 

36 

38.7 

25 

26 


64 

70.5 

73.6 

69.7 

87.0 

71-3 


35 
35 

% 

32 

32 


7 

8 

9 
10 
11 
12 
IS* 


Steam-jacket not in 
use. 


Throttled 




1.7666 

1-9833 

2.05 

2.1 

2.3166 

2.1667 
2.5666 


0.114 
0.139 
0.220 
0.271 
0.326 
0.413 
0.691 


5-92 
5-21 
3-73 
3-16 
2.72 
2.23 
1. 41 


36-5 
41. 1 
40-3 
41.8 
36 


70 

70 

70 

62 

64.1 

64 

73-3 


\ 

36.5 
36.9 
37 
33-8 

35 






14 
15 

16 
17 
18 
19 
20 
21 


Steam-jacket in use. 


2.0166 

2.05 

2.2 

2.21666 

2.0333 

3-75 

2.0833 

2.3 


0.105 
0.144 
0.155 
172 
0.221 
255 
0.378 
0.416 


6.08 
5-07 
4.82 

4-49 
3-71 
332 
2.40 
2.21 


19.7 

13-3 

19 

13 

22 

30.8 

40.9 

41 


69-5 
80 

74 

75-5 

76.5 

69.9 

65-9 

72.3 


34-4 
33 
35 
33 

34 
34 


22 
23 
24 
25 


Condensing without 
vacuum. 


Steam-jacket not J 

in use. | 

Steam-jacket in j 

use. 1 


2.2 

2.21666 
2.05 
2.1166 


0.178 
0.240 
0.196 
0.237 


4-37 
3-48 
4.07 
3-52 


45 

39-5 
40.4 
36 


77-3 
7a 

74-4 
74-6 


37 
34 


26 


Link hauled up. 


Without jacket and ) 
ind. cut off. f 


I. 91666 
2.06667 

1-95 


0.366 
0.243 
0.383 


2-47 
3-45 
2-37 


4 

28.3 

14-3 


65 
71.7 

86 


33 


27 


With 
jacket. 


With 1 
cut-off. f 


32 


28 


Without \ 
cut-off. ) 


33 


29 
30 
31 
32 


j- Jacket not in use, ] 
K Jacket supplied with steam from boiler. • 


2-5 

2.05 

1.8666 

2-0333 


0.151 
0.200 
0.153 
0.212 


4.91 
4.01 
4.87 
3-83 


40.4 
37-6 
4 

6.6 


64.4 
63-3 
75-6 
74 


33-6 
34 

33-4 
32 -5 


34* 
35 
36 
37* 


Steam-jacket not in use. 


23-95 
2.183^3 

2.0166 
1-9833 


173 
0.071 
0.123 
0.150 
0.185 


4.46 
7-78 
5-63 
4-94 
4-25 


20.9 

39-8 

46 

44-3 

36 


74.6 
67-5 
73-7 
72-3 
66 


36 
^1.6 


38 

39 

40* 

41* 

42* 

43 


Steam-jacket in use. 


23-9833 
2.2166 
2.0166 
2.1166 
4.41666 
1-9333 


0.171 
0.080 
0.122 
0.148 
0.173 
0.189 


4-50 

4-98 
4.61 
4.19 


37-8 

43 

57-5 

32.5 

48.6 

.39-5 


69.4 
75 


36 ' 
35.5 

II 

35 



TESTS OF SIMPLE AND COMPOUND ENGINES. 



277 



TABLE Will.— Continued. 





Temperatures, 
Fahrenheit. 


Pressures— pounds per square inch. 




Dis- 

ch'rge 
w'ter. 


Hot- 
well. 


Feed- 
water 

in 
tanks. 


Boiler 
pres- 
sure by- 
gauge. 


Vacu- 
um in 
con- 
denser, 
ins. of 
mer- 
cury. 


Baro- 
meter 


Initial 
pressu'e 
abso- 
lute. 


Ter- 
minal 
pres- 
sure 
abso- 
lute. 


Cush- 
ion 
pres- 
sure 
abso- 
lute. 


Back 
pres- 
sure 
abso- 
lute. 


Vacu- 
um at 
half- 
stroke 


Mean 
effec- 
tive 
pres- 
sure. 


1 

2 
3 

5 
6 


75 

80.25 

84 

78.3 

56.5 

56 


116. 6 
124.8 
118. 4 
123 

115-5 
II3-7 


115-7 
121. 8 
"9-3 
123-3 
103.7 
112. 3 


14.56 
12 83 
15 42 
13.14 
13.39 
13.86 


25-54 

25 

25.12 

24.88 

26.04 

^5-5 


14.8 
14.8 
14.7 
14.8 
15.0 
15.0 


25-3 
23-7 
26.3 
24.1 

23-9 
25.0 


11 .1 

13-1 
12.0 
13-8 
II. 7 
14.2 


8.7 
9.4 
9.6 
9-5 

9-2 

11. 


4.0 

r.5 


II. 7 
"•5 
11-5 
II. 2 
12.5 
12.0 


15-8 
16.1 
16.8 
16.8 
15-9 
17.7 


7 

8 

9 
10 
11 
12 
13* 


65 

69.7 
88.8 
72 
106 
79-3 


"5 

102.5 

III. 7 

128.4 

III. I 

147-5 

130.0 


103-7 

100.7 

107.6 

132.4 

108 

138.9 

122.8 


44.8 

40 9 

43.3 

39.4 

39.5 

37.67 

39.0 


25-9 
26.1 
25.9 
23.6 

25-9 
22.7 
24.6 


14.8 
14.8 

14.6 


56-3 
52-8 
55-8 
51-8 
52-3 
50-3 
44-7 


10.2 
10.6 
13.2 
14.0 
16.4 
19-3 
21.7 


8.0 
8.0 
8.4 

10.8 
8.3 

13-5 
8-3 


3-3 

3-4 

3-2 

4.4 
3-7 
5-5 
30 


11. 8 

11. 7 

11. 9 
10. 

11. 8 
10.4 
II. 7 


20.8 
21.0 

26.2 
26.5 
30.8 
30.9 
30-4 


14 
15 
16 
17 

18 
19 
20 
21 


61.7 

60.7 

77 

61.5 

80 

96.7 

74-4 

85 


98.3 
112 
109.6 
"5-5 
"5 
129.4 
III .1 
130 


102.5 

106.9 
110.2 
113.8 
123.6 
105.8 
123-5 


45.4 
42.8 
41 6 
43 9 
41.3 
40.0 
86.2 
37.4 


26.1 
26.5 
25-6 
26.6 

24.6 
26.4 
24.8 


14.8 
15-1 
14.8 

15-1 
14.8 
14.8 
14.8 
14.8 


58.0 
53-9 
54-6 
54-7 
54-7 
52-4 
49-3 
50.4 


9.8 
10.4 
10.3 
II-5 
II. 7 
13-5 
14.8 
18.9 


8.5 
II. 4 

8.7 
12.2 

9.8 
II. 4 
14.8 
10.6 


3-7 
3-4 

1:1 

3-8 
4.7 
2.9 
4-5 


II-3 
II. I 
II. 6 
12.0 
II-5 
10.7 

10.8 


19.9 
21.7 
21.7 
23.6 
24.6 
26.4 
28.5 
31-9 


22 
23 
24 
25 


••■• 




121. 7 
133-4 
126.8 
134-4 


70.7 
66.2 
69.7 
67.4 


I.O 

1-7 
1.0 
1-7 


14.9 
14.7 
14.8 
14.7 


83.7 

82.6 
78.8 


19-3 
21.5 
19.7 
21. 1 


41-3 

45-9 


14.9 
14.7 
14.8 
14.8 


•••• 


26.5 
28.9 
37.9 
29.0 


26 

27 
28 


83 

62.7 

65-7 


141 
116.3 
121. 3 


132.6 
112. 3 
122.3 


63.8 
69.6 
59.9 


24.7 
26.0 
25-3 


I5-I 
15-0 
iS-i 


66.9 
70.2 
63.6 


19.6 

I5-I 
18.8 


28.3 

25-5 
28.3 


6-7 
5-0 
6.0 


10.3 
II. 9 
II-3 


35-0 
32.1 
34-0 


29 
30 
81 
32 


78.8 
75 


114. 2 
no. 6 
130 
132 


109.6 
107.2 
121. 1 
126 


69.6 
60.4 
71.2 
67.0 


26.0 
25-8 
25.8 
25 4 


14.8 
14.8 
J5-I 
15-1 


82.4 

73-2 
82.6 
78.1 


15-7 
16.7 
14.0 
15-7 


9.2 
^0.5 
16. 1 
16.9 


3-3 
4.1 
4.2 
4.6 


II. 

11. 
II. 6 

11. 1 


35-0 
34-7 
31-8 
33-4 


33 

34* 

35 

36 

37* 


73-4 
75-5 

76.3 
68.3 


128.4 

119 

120.3 

111. 5 

112. 6 


123-7 
113-5 
117. 1 
109. 1 
107.6 


64 1 
71 5 

68.2^ 

68.5 

61.1 


25-3 
25.2 
25.1 

25-9 
25.8 


\n 
14.6 
14.8 
14.6 


76.1 

111 
81.7 
74.0 


15-4 
12.5 
14.2 

15-3 
16.2 


14.8 
10.6 
10.6 
9.9 
10.5 


4-3 
4-5 
4-7 
3-9 
4.0 


11-3 
10.3 
10.3 

II-5 
10.9 


32.4 
25.8 
30.1 
34-0 
34-7 


38 

39 

40* 

41* 

42* 

43 


72.4 

66 

77-5 

65.3 

75-4 

75-3 


120.5 

114 

122 

III. 3 
117. 9 
120 


"9-5 
1151 
117.9 
113-8 
120 

121. 6 


65.4 
71.6 
71.8 
69.9 
68.3 
67.2 


25-3 
25-7 
25.4 
25.8 
24.9 
25.0 


14.7 
14.8 
14.8 
14.8 
14.7 
14.8 


77-8 
85.0 
85.3 
83.5 
81.7 
80.7 


155 
12. 1 
15-5 
i6.6 
16. 1 
1-7-5 


12.3 
9-9 
10.5 
10.5 
12.3 
10.5 


4.0 
3-6 
4.2 
4.0 

4-2 

4-4 


II-3 
II-3 
II. 1 
11. 1 
II. 3 
II. I 


33-4 
28.0 
33-6 
36.5 

35-2 
36.9 



278 



THERMODYNAMICS OF THE STEAM-ENGINE, 



TABLE M\\\.— Concluded. 





Revolutions. 


Horse- 






Water 






Water per horse- 








power. 












power per hour. 




Total 
water 
from 
con- 
den- 
ser. 


Total 
water 

from 
jack's 

and 
steam 
chest. 


Propor- 
tion of 
water 
from 
jackets 
and 
steam 
chest. 


Water 
per 
hour. 


Propor- 
tion of 

total 
water 
shown 
by indi- 
cator. 




Total 


Per 
hour. 


Per 
min- 
ute. 


Indi- 
cated. 


Net. 
** 


Per 
indi- 
cated 
horse- 
pow'r 
meas- 
ured. 


Per 

net 
horse- 
pow'r 
meas- 
ured. 


Per 
indi- 
cated 
horse- 
pow'r 
by in- 
dica- 
tor. 


1 


4606 


2403 


40.1 


87.0 


73-2 


6722 






3512 


0-635 


40.4 


47-9 


25.6 


2 


5517 


2452 


40.8 


go. 2 


7b. I 


8949 






3982 


0.673 


44 2 


52.3 


29-7 


3 


S199 


2476 


41-3 


95-3 


81. 1 


6716 


177 


0.026 


3175 


0.779 


33.3 


39-2 


26.0 


4 


5434 


2547 


42-5 


97-9 


83-3 


7827 


165 


0.021 


3660 


0.871 


37.4 


43-9 


32. b 


6 


5468 


2467 


41. 1 


89-7 


75.5 


6740 


292 


0.043 


3054 


0.789 


34.1 


40.4 


26.9 


6 


5580 


2536 


42.3 


102.9 


88.4 


7849 


243 


0.031 


3588 


0.830 


34.8 


40.6 


28.9 


7 


45^8 


2580 


43 


122.8 


108. 1 


5618 






3^95 


0.688 


26.0 


29.6 


17.9 


8 


5264 


2654 


44.2 


127.2 


112. 


6745 




.... 


3397 


0.692 


26 7 


30-3 


18.5 


9 


6245 


3046 


50.8 


182.2 


164.8 


8980 






4373 


0.762 


24.0 


26.5 


18.3 


10 


b^i8 


3009 


50.1 


182.4 


165 - = 


10039 


.... 


.... 


4800 


0.725 


26.3 


29.1 


19. 1 


11 


7787 


3361 


56.0 


236.9 


217,7 


13468 






5800 


0-795 


24 5 


26.6 


19-S 


12 


7248 


3345 


55-8 


236.5 


217-3 


14474 







664 s 


0.790 


28.1 


30. b 


22.2 


18* 


8113 


3161 


52.7 


219.5 


201.4 


16736 


.... 




6493 


0.882 


29.6 


32.2 


26.1 


14 


5363 


2659 


44-3 


121. 1 


105.9 


5618 


■^16 


0.092 


2778 


0.780 


22.9 


26.2 


17.9 


15 


5665 


2763 


46.1 


137-5 


I2X.4 


6731 


428 


0.066 


3295 


0.717 


24.0 


27.1 


17.2 


16 


6064 


2753 


45-9 


136.4 


120.7 


6736 


321 


0.048 


3055 


0.777 


22 4 


25-3 


17.4 


17 


6691 


3018 


50-3 


163-3 


146.0 


8974 


416 


. 0.047 


4055 


0.702 


24.8 


27.8 


17.4 


IS 


6003 


2952 


49.2 


166.2 


149-3 


7846 


332 


0.042 


3852 


0.742 


23.2 


25-8 


17.2 


19 


11509 


3069 


51.2 


185.2 


167.5 


17899 


553 


0.031 


4761 


0.721 


25.7 


28.4 


18. s 


20 


6816 


3272 


54-5 


213.0 


194-3 


11229 


300 


0.027 


5388 


0-753 


25.3 


27.7 


19.0 


21 


8038 


3495 


58-2 


255-0 


235-0 


15654 


290 


0.019 


6763 


0.808 


26.5 


28.8 


21.4 


22 


6164 


2801 


46.7 


169.6 


153-6 


11186 






6165 


0.796 


30.0 


33-1 


23-9 


28 


6873 


3101 


51-7 


204.8 


187.1 


13382 






6901 


837 


29.4 


32.1 


24.6 


24 


bo8,s 


2968 


49-5 


189.6 


172.6 


10054 


288 


0.029 


6085 


0.940 


25.9 


28.4 


22.2 


2b 


6761 


3194 


53-23 


212.2 


193-9 


12263 


429 


0.035 


6752 


0.864 


27.3 


29.9 


23.6 


26 


7128 


3719 


62.0 


297.8 


276.5 


14500 






7515 


0.757 


25.2 


27.2 


19. 1 


27 


7268 


3517 


58.6 


258.5 


238-4 


12334 


517 


0.042 


5946 


0.695 


23 


24.9 


16.0 


28 


7131 


3657 


60.9 


284.2 


263.2 


13422 


374 


0.028 


6873 


0.783 


24 2 


26.1 


18.9 


29 


9037 


3615 


60.2 


289.2 


268.5 


15707 


416 


0.026 


6287 


0.750 


21.7 


23-4 


16.3 


80 


7402 


2611 


60.2 


286.8 


266.2 


13470 


234 


0.017 


6578 


0.758 


22.9 


24.7 


17.4 


81 


6^48 


3So8 


S8.=; 


255.3 


235.2 


1H18 


459 


0.041 


5994 


0.660 


23.5 


25-5 


15-5 


82 


7513 


3695 


61.6 


282.5 


261.4 


14526 


301 


0.021 


7157 


0.654 


25.3 


27.4 


16.6 


33 


86041 


3630 


60.5 


268.6 


247.9 


155413 






6541 


0.696 


24.3 


26.4 


16.9 


84* 


6858 


3141 


52.4 


185.1 


167. 1 


10088 




.... 


4633 


0.699 


25.0 


27-7 


17-5 


8b 


6890 


3361 


56.0 


231.4 


212.2 


11199 







5501 


0.716 


23.8 


29.9 


17.0 


86 


7244 


3592 


59-9 


279.6 


259.0 


12343 






6120 


■ 0.748 


21.9 


23.6 


16.4 


87* 


707s 


3567 


59-5 


282.9 


262.5 


13469 






6786 


0.707 


24.0 


25.8 


17.0 


38 


885S2 


3692 


61.5 


281.6 


260.5 


148863 


5157 


0-035 


6208 


0-757 


22.0 


23.8 


16.7 


89 


6798 


3067 


5I-I 


197.0 


179-5 


8962 


460 


0.051 


4036 


0.765 


20 5 


22.5 


15-7 


40* 


7089 


3515 


58.6 


270.4 


250.3 


liiqb 


408 


0.036 


5573 


0.811 


20.6 


22.3 


16.7 


41* 


7774 


3672 


61.2 


306.2 


285.3 


13450 


384 


0.029 


6336 


0.797 


20.7 


22.2 


16.9 


42* 


16234 


3&7& 


61.3 


295.6 


274.6 


27978 


935 


0.033 


6331 


0.847 


21.4 


23.1 


18. 1 


43 


7972 4123 


bb.7 


348-0 


324.4 


14542 


453 


0.032 


7475 


0.800 


21.5 


23.0 


17.2 



♦* Estimated friction 2.5 pounds per square inch. 



TESTS OF SIMPLE AND COMPOUND ENGINES. 279 

with the cyHnder thoroughly steam-jacketed. The gain from 
compounding is 



20.7 — 184 

207 ='^-"+ 



when the consumptions of steam are compared directly, and is 

2 1 900 — 19600 

— = 0.1 1 — 

21900 

when the thermal units per horse-power per hour are com- 
pared. 

If the test on the Rush is compared with the test on the 
Reynolds-Corliss engine the gain is a little less, but the latter 
engine has the advantage of much higher boiler-pressure. 

The engine of the BacJie, although it uses steam of 80 pounds 
boiler-pressure, appears to require nearly ten per cent more steam 
per horse-power per hour than the Rush does, and to use nearly 
as much steam as the Reynolds-Corliss engine working single 
and without a steam-jacket. In this comparison it is to be borne 
in mind that the engine of the Bache was a tandem compound 
engine, having a steam-jacket on the large cylinder only, while 
the engine of the Rusk was a receiver compound engine, with 
the cranks at 90°, and with both cylinders thoroughly jacketed. 
From the arrangement of the cylinders the radiation was prob- 
ably much less than the radiation from the engine of the Bache, 
Also, the engine of the Bache was considerably smaller than 
that of the Rush. A part of the inferiority of the engine of 
the Bache should be attributed to the forms of the boilers. 
The boiler of the Bache was designed to give high evaporation, 
consequently the steam in the steam-chimney did not receive 
much heat from the escaping gases. On the revenue steamers 
the boilers were designed to give large power for a given space, 
and the escaping gases in the steam-chimney had a higher 
temperature, and consequently the steam furnished was prob- 



28o 



THERMODYNAMICS OF THE STEAM-ENGINE. 



ably drier. It appears, therefore, that the larger cost of fuel 
per pound of steam made when the proportion of heating 
surface is smaller, may be compensated in part by a smaller 
cost of power in pounds of steam, on account of superior dry- 
ness. 

In these experiments, however, the higher evaporative 
efficiency of the boilers of the Bache more than compensated 
for the greater cost of power in pounds of steam, as the follow- 
ing table will show : 





Bache. 


Rush. 


Water per horse-powerper hour 


20.332 

9-131 
2.227 


18.384 
7-549 
2.435 


Water evaporated per pound of coal • . 


Coal per horse-power per hour 





The consumption of coal in case of the Bache was calcu- 
lated from the performance of the boiler during the long run 
(Table VI, Exp. 9), assuming the efficiency of the boiler to be 
the same. 

The gain by compounding in practice is frequently claimed 
to be twenty per cent, for which Mr. Emery gives the following 
explanation : In high-pressure condensing engines the pressure 
is seldom maintained at the point designed. This occurs from 
two causes — the carelessness of operating the engine, or the 
imperfect adaptation of the engine to the purpose. No matter 
what the pressure designed may be, if the engine is designed 
to work with considerable expansion, the engineer finds that 
his engine works more smoothly, and with less trouble to him- 
self, with less pressure and less expansion, and for trivial rea- 
sons lets his pressure fall or partially closes the throttle, and 
lengthens the cut-off, and finally believes that it is as well to 
work in that way all the time. With compound engines there 
are fewer difficulties in working high-pressure steam, and in 
most cases it is difficult to keep up the speed with low pres- 
sures. 

The efficiency of the boilers of the several steamers was 



TESTS OF SIMPLE AND COMPOUND ENGINES. 



281 



tested by one experiment on each, of sufficient length for the 
purpose. The results are given in the following table : 

Efficiency of Boilers. 



Bache, Table VI, Exp. 9 

Rush, Table VII, Exp. i 

Dexter. Table VII, Exp. 5... 
Dallas, Table VII, Exp. 12 . . . 
Gallatin, Table VIII, Exp. 38 



Coal per sq. 

foot of grate 

surface per 

hour. 



8.84. 
11.388 
12.026 
13-313 
15-305 



Per cent 
of refuse. 



19.8 

20.978 

20.291 

20.503 

21.609 



Water evap- 
orated per 
pound of coal 
from and at 



8.5675 
8.6878 
8.7625 
7.418 



Coal per 

horse-power 

per hour. 



•451 

•4352 

■1313 

.4267 

.002 



If we compare the tests stated in the table on page 270, it 
appears that the use of a steam-jacket on the BachCy when 
working single, was accompanied by a gain of 



27600—24700 
27600 



0.10 + , 



while the use of a steam-jacket on the Gallatin was accompa- 
nied by a gain of 



23200 — 21900 
23200 



= o.io — 



In Experiments 29 and 30 on the Gallatin the steam-jacket 
was not in use, but the condensed water was drained from the 
valve-chest — probably through the pipe which ordinarily sup- 
plied the jacket when it was in use. In Experiments 31 and 
32 the jacket was supplied with steam directly from the boiler, 
and presumably the valve-chest was not drained. Comparing 
these experiments with each other and with Experiment 41, it 
appears that the draining of the steam-chest was of more im- 
portance than the use of a steam-jacket. In some engines the 
whole supply of steam for the engine is passed through the 
steam-jacket on the way to the steam-chest ; and in such case 
the steam must suffer condensation in the jacket, and enter 
the cylinder with more moisture than if it passed directly to 
the steam-chest. Such engines do not show so good economy 
as those having a separate supply of steam to the steam-chest. 



282 " THERMODYNAMICS OF THE STEAM-ENGINE. 

The gain from the use of a steam-jacket on the large cylin- 
der, only, of a compound engine is shown by comparing the 
experiments on the Bache working compound, with and with- 
out the jacket in use. The gain is 

24500—21700 

-^ : — = 0.1 1 + . 

24500 ' 

The experiments do not give the data for the discussion of 
the saving by the use of a steam-jacket on a^ compound engine 
when both cylinders are steam-jacketed. Should we compare 
the test on the Bache without the jacket in use with the test 
on the Rush with both cylinders jacketed, it would appear that 
there is a great gain from jacketing both cylinders, and that 
there is a marked gain from applying a steam-jacket to the 
small cylinder in addition to that on the large cylinder, but 
from the preceding discussion it is evident that such a com- 
parison would be illusive. It does not appear probable that 
the jacketing of both cylinders of a compound engine would 
give a greater gain than the jacketing the cylinder of a simple 
engine ; and if such a conclusion is admissible, then those 
experiments appear to show that the appUcation of a jacket to 
the large cylinder only of a compound engine gives as great a 
gain as the gain from jacketing the cylinder of a simple engine, 
and that consequently there would be little or no gain from 
applying a jacket to the small cylinder in addition to one on 
the large cylinder. On the other hand, Rankine ^ states that 
in cases where a steam-jacket has been applied to the small 
cylinder only the heat thus applied has been found sufficient ; 
but Rankine gives this statement in connection with a wrong 
theory of the action of a steam-jacket, i.e., that it prevents 
liquefaction in the mass of the steam during expansion, and he 
does not quote experiments to substantiate the statement. We 
must consequently await further experiments on this point. 

It may be of interest to state in this connection that a steam- 
jacket is sometimes applied to the intermediate cylinder only 

* Steam-engine, page 396. 



TESTS OF SIMPLE AND COMPOUND ENGINES, 



283 



of a triple-expansion engine, and that some engineers are in 
the habit of using the jacket in starting the engine, but not 
when the engine is working under normal conditions. 

The only series of tests that can be used to determine the 
number of expansions to be used with a compound engine are 
those on the Bache, which show that the best economy was 
attained with 6 or 7 expansions both when the jacket on the 
large cylinder was in use, and when it was not in use. 

To show the gain from increased steam-pressure, the follow- 
ing table has been made. The greater economy of the engine 
of the Gallatin as compared with that of the Dexter may be 
attributed in part to the larger size of the former. 

Steam-pressure and Cut-off, Simple Engines. 



Michigan. 
Mackinaw 

Eutaw 

Dexter 

Dallas.... 
Gallatin.. 



Boiler- 
pressure 
gauge. 



Cut-off 

fraction of 

stroke. 



Steam per 

horse- 
power per 
hour. 



33-1 
30-3 
30.6 

23-9 
26.9 
40.4 
24.0 
21.9 



Thermal 
units per 

horse- 
power per 

hour. 



25400 
27500 
42100 
25400 
23200 



Relative 
economy 






67 









Qi 





as 





55 





90 


I 


00 



Tests on the Leila, the Siesta, and the Gleam. — The 

engines of the yachts Leila and Siesta were built by the 
Herreshoff Manufacturing Co., and were tested in Narragansett 
Bay by Mr. Isherwood "^ in 1880 and 1882. The engine of the 
yacht Gleam was built by the Fore River Engine Co., of 
Weymouth, Mass., and was tested by Messrs. Roberts f and 
Sayer of the Class of 1888, Massachusetts Institute of Tech- 
nology. 

The engines of the Leila and Siesta differed only in size, 
those of the latter being a little the larger. They each had 
two cylinders; — one high-pressure and one low-pressure, — with 
the cranks at right angles. Both cylinders of each engine had 



* Reports to the Bureau of Steam Engineering, 
f Thesis, 1888. 



li and 1S83. 



284 



THERMODYNAMICS OF THE STEAM-ENGINE. 



a plain slide-valve with a cut-off valve on the back of the main 
valve, the main valves having neither lead nor compression. 
The cylinders were lagged, but not steam-jacketed. The boiler 
of the Leila was arranged to furnish strongly-superheated steam, 
but that of the Siesta furnished saturated or moist steam. 

In the tests on the Leila the condensed steam from the sur- 
face condenser was measured, as it was delivered by the air- 
pump, in a standard-gallon measure. The condensed steam 
from the surface condenser of the Siesta was measured in two 
measuring-tanks of known capacity, which were filled and 
emptied alternately. 

The engine of the Gleam had two cylinders with the cranks 
at right angles. The cylinders were lagged, but not steam- 
jacketed. Each cylinder had a piston slide-valve actuated by 
a Joy valve-gear. Steam was furnished by an upright tubular 
boiler which superheated the steam enough to determine its 
quality, but not enough to affect the economy of the steam 
consumption to any marked degree. 

The dimensions of the engines of these three yachts are 
given in the following table : 

Dimensions of Yacht Engines. 



Number of cylinders 

Diameter, small cylinder, inches 

large cylinder, " 

piston-rod, small cylinder, inches 
" large " " 
Stroke, both pistons 

Displacement, small cylinder, cubic feet 

larg-e " " " .... 

Clearance, fraction of piston displacement- 
small cylinder 

large cylinder 

Ratio of volumes of cylinders 



Leila 


Siesta. 


2 


2 


9 
i6 

i8 ^ 


■2 

18 ^ 


0.652 
2.034 


0.891 
2.634 


0.088 
0.068 


0.094 
0.069 


3.196 


2.962 



Gleam. 



9-035 
15-71 



11.96 



Head -end. 

0.444 
1.342 



0.042 
0.024 



Crank-end. 

0-443 
1.340 

0.04s 
0.026 



3.026 



The data and the results of the tests on the yachts Leila^ 
Siesta, and Gleam are given in Tables IX, X, and XI. 

Discussion of Results. — The tests on the engines of the 
Leila, lettered A to H, were made with substantially the same 
cut-off and the same number of total expansions. The steam- 



TESTS OF SIMPLE AND COMPOUND ENGINES. 285 

pressure was diminished progressively, accompanied by a 
diminution of the amount of superheating and of the speed of 
revolution. The change from 95 revolutions per minute to 
220 revolutions per minute is not enough to produce a marked 
change of economy ; consequently, the regular and marked 
increase of steam consumption, or of the consumption of ther- 
mal units, per horse-power per hour is due to the decrease of 
pressure and the less amount of superheating. 

The remaining experiments were made to determine the 
effect of cutting-off on the small cylinder only, on the large 
cylinder only, and of not cutting-off on either cylinder. Also 
the gain in this engine from compounding. 

Comparing the Experiments C and I, which are in other 
respects alike, the consumptions of thermal units per horse- 
power per hour, with and without a cut-off on the large cylinder 
in addition to the cut-off on the small cylinder, are in the ratio of 

19100 : 21000 :: I : 1.099. 

In the first series it is noticeable that the distribution of 
work between the two cylinders of the engine is good, and is 
not greatly affected by the change of pressure and of super- 
heating. In the tests I, J, and K an excessive amount of 
work is done in the small cylinder. On the other hand, the 
work done in the large cylinder is excessive in the tests L and 
M, when the steam is cut off in the large cylinder only. 

The total number of expansions is not affected by the cut- 
off in the large cylinder, and is nearly the same for experiments 
C and I. The gain from the cut-off on the large cylinder is to 
be attributed to the diminution of the drop between the high- 
and low-pressure cylinders and to the better division of the 
ranges of temperatures. 

When the steam was cut off in the large cylinder only the 
total number of expansions depended on the ratio of the vol- 
umes of the cylinders only, and was much less than when the 
steam was cut off in the small cylinder, and the increased con- 
sumption is to be attrib;*<<Led mainly to this cause. 



286 



THERMODYNAMICS OF THE STEAM-ENGINE. 



TABLE 

Tests on 







t 


Cut-off and 


Temperatures 


, 


Pressures, pounds 


□n the 




Manner of 


a 


expansions. 


bahrenheit. 




sqijare 


inch. 






H 


t. 


II 


% 




1 


a 


in 


<u 

3 

03 • 




25 


en 




Running. 


G 

.2 

"3 




o;c 


a 






a: rt j_. 




.2 >, 

T3X1 


aa 


a^ 

§a 






^ 


3 y 


3 


<u 


H-. O. 


>+-l 


>+-( 


HH^ 


M_ t5 «3 


o-^ 


1^ V. 


rt ° 


rt 






^ 


U 


U 


H 

















m 




pq 


> 


A 




2-2T..S 


0.4 


0.361 


7.12 


42 


49 


95-0 


417 


355-2 


129.4 


20.7 


30.25 


25.83 


B 


Steam cut off 


215-9 


0.4 


0.336 


7.12 


45 


4Q 


93-5 


416 


354-0 


127.2 29.0 


30.25 


26.07 


€ 


in both 


192.2 


0.350 


0-33S 


7.93 


55 


52 


76.3 


378 


340.6 


104.5, 18.2 


30.00 


25.92 


1> 


cylinders by 


181. 1 


0-335 


0.346 


8.21 


50 


47 


71.0 


366 


332.0 


91.4; 15.9 


29.98 


25-49 


E 


independent 


166.5 


0336 


0.371 


8.21 


54 


51 


68.0 


3 so 


319.9 


75.0 10.5 


30.03 


26.32 


F 


cut-off 


145-5 


0-353 


0.368 


7.89 


47 


52 


64.0 


320 


302.3 


57.71 5.5 


30.00 


26.50 


« 


valves. 


III. 5 


0.358 


0.376 


7.V9 


47 


S2 


60.0 


279 


377-1 


32.4 


-0,8 


30.00 


26.50 


H 




94-7 


0.361 


0-349 


7.74 


52 


47 


64.0 


261 

383 


361.0 


21.3 


-2.4 


30.00 


25.18 


T 


Steam cut off 


188. 1 


0.329 




8.35 


43 


46 


76.0 


340.2 


103.7 


— O.I 


30.36 


24.41 


J 


in small cylin- 


167.3 


0.325 





8.42 


44 


47 


6q.5 


3S6 


3197 


74.6 


- 3-5 


30.36 


25.18 


K 


der only. 


145-9 


0-347 




7.99 


44 


47 


64-5 


335 


303-4 


55.8 


-5-2 


30.36 


25-58 


L 

M 


Steam cut off 
in large cylin- 
der only. 


197.9 
122.5 


.... 


0.297 
0.363 


3.20 
3.20 


38 
50 


48 
47 


88.5 
64-5 


360 
304 


308.4 
260.5 


61.7 
21.0 


33-4 
8.0 


29.88 
30.06 


25.43 
25-93 


U 


No cut-off. 


189.5 




.... 


3.20 


43 


47 


91.0 


345 


304-6 


57 


4-9 


30.36 


25-05 




Small cylin- 
der discon- 































nected; large 


191-5 




0.335 


2.66 


38 


47 


96.5 


344 


292.3 


44.9 


40.7 


30-17 


25-59 


!» 


cylinder used 

as a simple 

engine. 


147.6 




0-371 


2.43 


40 


47 


71.0 


304 


261.4 


21.4 


19.4 


30.19 


25.98 



In Experiment N the omission of the cut-off on both cylin- 
ders gave a fair distribution of the work, but the drop between 
the cyhnders was excessive, and the consumption was larger, 
and the engine was consequently less economical than when 
the large cylinder was used alone, as in the Experiment O. 

The gain from compounding may be inferred from a com- 
parison of Experiments G and H with Experiments O and P ; 
but a correct conclusion cannot be reached from these experi- 
ments, nor from a comparison of any of the tests in the table, 
since, on the one hand, the economy of the large cylinder used 
as a simple engine would be improved by an increase of pressure 
and an increase of the total number of expansions ; and, on the 
other hand, the steam-pressure in Experiments G and H is too 
low to make compounding advantageous. 



TESTS OF SIMPLE AND COMPOUND ENGINES. 



287^ 



IX. 

Leila. 



— 


Pressures, pounds on the square inch. Horse-power| 


to 

If 


3 


Percent of 






indicated. 


11 


steam in the 




IT \- A U t 


cylinder. 






x^.aigc »,yiniuci, au3wiun_. | 












-. (U , 1 


1 












^ 


1^ 




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a 


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Si 



kJ i-i 

60.8 


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1 


> 


v. 

0. 

is 


Oh 


a 
u 

Jio 
3 is 

^0 


u 


C V 


> 

h 


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-a 
c 

6 


■a 
c 




be 

u 
bfi 

< 


as 

sa 




B u 
3 

u 




to >> 



V 


A 


T34.8 


118. 9 


48.7 


44-7 


S3-8 


4S.S 


32.0 


1^.3 


4-7 


6.5 


20.4 


... 


82.2 


149.9 


16 4 


18400 


08 


*I02 


81 


H 


130-7 


118. 6 57-1 


46.7 


42-5 


53-4 


44.1 


33.0 


12.7 


4.8 


6.1 


20.3 


65.6 79.6 


145-2 


16.0 


18100 


90 


*I03 


80 


r 


109.0 


100 . 4 ' 4.0 . 6 


33-2,29.7 


44-3 


32.0 


23.1 


9-7 


4.1 


4.8 


14-7 


48.451-5 


99.9 


16.7 


19100 


87 


93 


76 


T> 


97.6 


92.5'38.8 


32-3I28.8 


SQ - S 


29.6 


20.6 


8.8 


4.1 


4-3 


13-7 


4o.7;45-i 


85-8 


17.4 


20000 


81 


93 


72 


F. 


8^7 


77-6 32-3 


25.3122.4 


33 -.S 


23.8 


16.3 


7-6 


3-3 


3-7 


10.54 


3^-7131-9 


63.6 


18.7 


21400 


80 


91 


74 


F 


6,1 6 


58. 826. 2 


20.0 17.0 


26.2 


19-0 


16.4 


6.4 


3-3 


3-6 


8.05 


21. 721. 3 


43-0 


20.9 


23900 


67 


78 


64 





42.5 


33.9'i8.8 


13-711-9 


17.8 


12.2 


8.9 


,S-o 


3-3 


3-4 


4-63 


11-3 9-4 


20.8 


25.0 


28400 


66 


49 


45 


H 


323 


30- 5 


16.6 


12.6 11.6 


12.8 


II. I 


8.6 


5-3 


4.0 


4-3 


3.40 


6.9 5.9 


T2.8 


32.7 


37000 


56 


78 


83 


T 


114. 2 


[07.0 


43-0 


16.815 2 


63.6 


13.6 


.... 


10.9 


5-0 


5-5 


7.50 


68.125.6 


93-7 


18.5 


21000 


87 


q6 


80 


J 


87-3 


80.8 


33 -S 


13.5 12.6 


47-7 


10.9 




9.2 


4-4 


4-9 


4.88 


45-5,14-8 


60.3 


20 1 


23000 


83 


06 


85 


K 


66.7 


61.0 


26.5 


II. 6 


10.7 


36.6 


8-3 




7-5 


4.4 


4-7 


3-33 


30.4 8.8 


39-2 


23.9 


27300 


75 


86 
*II3 


80 


T. 


77-5 




66.4 


so. I 


44-'; 


20.1 


48.2 


38.5 


14.2 


3-7 


5-3 


23-6 


22.6:85.1 


107.7 


21.0 


23500 


85 


M 


331 




31.6 


22.5 


19.6 


18. 1 


21.4 


I5-I 


7.2 


3-5 


3-6 


9-25 


12.6 


20.6 


33-2 


28.6 


32300 




83 


64 


» 


70.6 




63.1 


22.6 


20.2 


43-9 


19-3 




i6.o 


4-5 


6.0 


10.80 


47-3 


37-2 


84.5 


28.1 


314O0 




*ios 


86 



P 














54-5 
30-9 


43-7 
24-9 


17.2 
10. 9 


4-3 
4.1 


6 T 


28.4 




98-c 
42-4 


98-c 

42.^ 


25.5 


2820C 






li 


.... 








.... 


.... 


4.6 


15-8 




32 


3570( 


► ... 





* Superheated. 

The tests on the Siesta were made primarily to determine 
the most advantageous cut-off for the large cylinder. Now the 
cut-off of the large cylinder does not affect the total number 
of expansions, nor does it affect the aggregate horse-power of 
the engine seriously. It does affect the pressure in the inter- 
mediate receiver, and consequently affects the division of power 
between the two cylinders, the drop between the cylinders, and 
the division of the range of temperatures. In comparing tests, 
those should be chosen in which all essential data except the 
cut-off of the large cylinder are substantially the same. 

The indicator-diagrams for the tests B and C are shown by 
Figs. 57 and 58. In the first the cut-off of the large cylinder 
is at 0.251 of the stroke, and the steam in the small cylinder is 



288 



THERMODYNAMICS OF THE STEAM-ENGINE. 



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TESTS OF SIMPLE A AD COMPOUND ENGINES. 



289 



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290 



THERMODYNAMICS OF THE STEAM-ENGINE. 



expanded down to the back pressure in that cylinder. The 
initial pressure in the large cylinder is the same as the back 
pressure in the small cylinder at half-stroke, and is greater than 




Fig. 57. 




Fig. 58. 



the terminal pressure in the small cylinder. This peculiarity of 
the back pressure in the small cylinder is due to the fact that 
the cranks of the engine are at right angles. In the test C, 
which has the cut-off at 0.465 of the stroke, there is a drop of 



TESTS OF SIMPLE AND COMPOUND ENGINES. 29I 



about 4J- pounds from the terminal pressure in the small cylin- 
der to the initial pressure in the large cylinder ; owing to the 
rise of back pressure in the small cylinder at half-stroke, the 



EXPERIMENT E. 

SMALL CYLINDER 





EXPERIMENT T".. 

SMALL CYLINDER. 

Scale ,80 lbs. -= 1 inch. 





Fig. 6o. 

drop at the end of the stroke of the small piston is greater than 
this, as is evident from the diagrams, Fig. 58. The ratio of the 
consumption per horse-power per hour is 

21600 : 20500 :: 1.05 : I 
in favor of Experiment C. 



292 



THERMODYNAMICS OF THE STEAM-ENGINE. 



A similar comparison can be made of the Experiments E 
and F. In Experiment E the cut-off is at 0.237 of the stroke 
of the large piston, and the expansion in the small cylinder is 
carried down to the back pressure. In Experiment F the cut- 
off is at 0.452 of the stroke of the large piston, and there is a 
drop of about 4^ pounds from the final pressure in the small 
cylinder to the initial pressure in the large cylinder, but, as 
with Experiment C, the drop at the end of the stroke of the 
small piston is more than that. The ratio of the consump- 
tions is 

21000 : 20500 :: 1.025 : i 

in favor of Experiment F. 

These two comparisons show that for this engine under the 
given circumstances the cut-off on the large cylinder should 
be at a little less than half-stroke instead of at about quarter- 
stroke, and that a small drop at the end of the stroke of the 
small piston is permissible. 

The diagrams for the Experiment H are shown by Fig. 61. 
In it the cut-off of the large cylinder occurred at 0.857 of the 

EXPERfMENT H. 

StVALL CYLINDER. 

Scale.CO Ibs.-^-l inch. 




LARGE CYLINDER. 

Scale,4:0 lbs. = 1 inch. 



Fig. 6i. 

stroke, and there was a drop of about I5|- pounds from the 
final pressure in the small cylinder to the initial pressure in the 
large cylinder. Compared with Experiment F, the consump- 
tions are in the ratio 



23400 : 2050^ 
in favor of the Experiment F. 



1. 14 : I 



TESTS OF SIMPLE AND COMPOUND ENGINES. 293 

The conclusion is that a small drop is allowable or even 
advantageous, but that a large drop is deleterious. 

The determination of the most advantageous number of 
total expansions is made difficult by the varying boiler-pressure. 
It is, however, apparent that 5.9 expansions in Experiment D 
gave a better economy than 12.9 expansions in Experiment A, 
although the steam-pressure in A was higher than in D. 

Inspection of Table X shows that six expansions reduce 
the pressure at the end of the stroke in the large cylinder to 
about ten pounds absolute. It is probable that a greater num- 
ber of expansions would not give greater economy for this 
engine with the given steam-pressure, though this fact cannot 
be conclusively shown from the tests given. 

If Experiment D on the Siesta, with 5.9 expansions and 
using saturated steam, may be compared with Experiment D on 
the Leila, with 8.1 expansions and using superheated steam, then 
it appears that the small amount of superheating in the latter 
had less effect than other causes that are commonly considered 
to be of secondary importance, since the test on the Siesta 
shows the better economy. 

The tests on the Gleam were made with the boiler-pressure 
very nearly constant, while the change in the speed of revolu- 
tion was too small to produce much effect. The throttle-valve 
was wide open during all of the tests, and the power of the 
engine was varied by changing the cut-off on both cylinders 
simultaneously. The tests i and 2, 3 and 4, and 5 and 6, were 
made under similar conditions for each pair. The last test, 
number 7, was made with full engine-power, at which the 
boiler was unable to furnish steam without undue forcing. The 
consumption of steam for the five last experiments is nearly 
constant, the variation in consumption under like conditions 
being as great as at the different rates of expansion from 4.39 
to 7.04. The consumption for 10.81 appears to be somewhat 
more than for a less rate of expansion. 

Leavitt Pumping-engine.* — Two duty tests of a com- 

* E. D. Leavitt, Jr., Boston Soc. Civ. Eng., 1885. 



294 THERMODYNAMICS OF THE STEAM-ENGINE. 

pound pumping-engine at the Boston Main Drainage Works 
are given here as an example of advanced practice. 

The engine is one of a pair of two-cylinder compound beam- 
engines. The steam-cylinders are inverted, and act on oppo- 
site ends of a short beam on a level with the engine-room 
floor ; below the floor are two single-acting plunger-pumps, 
connected one to each end of the beam, directly under the 
steam-cylinders. The main shaft carrying the fly-wheel is mid- 
way between the lower ends of the steam-cylinders, and the 
crank is connected to one end of the beam near the point of 
attachment of the links from the steam-piston and the pump. 
The steam from each end of the high-pressure cylinder passes 
through a straight passage to the same end of the low-pressure 
cylinder, and in these passages are reheaters made of brass 
tubes suppHed with boiler steam, through which the exhaust 
steam from the high-pressure cylinders passes, and by which it 
is dried or slightly superheated. The steam for the high-pres- 
sure cylinders is not superheated, but during the tests was 
assumed to be dry and saturated. 

The diameter of the high-pressure cylinder is 25-J inches, 
and that of the low-pressure cylinder is 52 inches; the stroke 
of each piston and of the pump-plungers is 4 feet. 

Each steam-cylinder has four independent valves, operated 
by cams ; the cams which move the admission-valves of the 
high-pressure cylinder are controlled by a governor. All the 
other valves have a fixed motion. 

The following description of the tests is taken from Mr, 
Leavitt's paper : 

The engine tested is known as Engine No. 3, and was sup- 
plied with steam from Boiler No. 2. 

The intended duration of each test was twenty-four hours. 

The method of making the tests was as follows : Steam was 
raised in the boiler until the pressure was sufficient to run the 
engine. The fires were then drawn, the ash-pits carefully 
cleaned, and new fires were started. It was desired to deter- 
mine the quantity of water pumped, by actual measurement, 
in the reservoir at Moon Island, and since stopping the engine 



TESTS OF SIMPLE AND COMPOUND ENGINES, 295 

would have caused large fluctuations of level in the connecting 
sewers, and so prevented accuracy of measurement, it was de- 
cided to keep the engine running at a constant rate. This was 
done by furnishing the engine with steam from Boiler No. 3 
until a few minutes after the new fires were started, when, by 
operating the valves rapidly and simultaneously. Boiler No. 3 
was shut off, and the engine took steam from No. 2, thus be- 
ginning the engine test. The engine counter was read at the 
instant the test began, and the other necessary observations 
were taken. The steam-pressure was increased from about 70 
pounds at the start, until it reached 100 pounds, at which it 
was kept constant until near the end of trial, when the fires 
were burned as low as possible, the steam pressure dropping 
in consequence. When the pressure and height of water in 
the boiler were the same as at the beginning of the experiment, 
the final observations were taken, and the fires were drawn. 
The refuse was then spread upon the floor to cool. The un- 
burnt coal was picked from the ashes and weighed. This 
weight (averaging less than one per cent of the total coal) was 
deducted from the gross amount of coal charged. The valve 
between Boiler No. 2 and Boiler No. 3 is supposed to have 
been tight, but to avoid increasing the duty by any leakage, the 
pressure in the latter was kept lower than in the former. 

The height of the sewage in the pump-well was determined 
by a float-gauge, tested before each trial ; the load on the 
pump by a mercurial gauge, attached to the force-main of an- 
other engine. This gauge represented the height in the pipe- 
chamber at the end of the force-mains, and, to get the actual 
pressure pumped against, it was necessary to add the friction 
in the force-main used. During the second test the actual 
pressure against which the pumps were working was measured 
by the elevation of the surface of water in a box at the top of a 
pipe connected with the force-main a few feet from the pump. 
A comparison of this gauge with the mercurial one gave a cor- 
rection for friction in the force-main to use with the first test. 

Dry Cumberland coal from the Pocahontas Mine was used 
during the trial. It was fed to the boiler from a car holding 



296 THERMODYNAMICS OF THE STEAM-ENGINE. 

about 1200 pounds. During the first test the car and contents 
were reweighed at the end of each half-hour, and during the 
second test after each firing. 

The steam-pressures at the boiler and the pressures and 
vacuum at the engine were determined by Bourdon gauges, 
which had been previously tested. 

The temperature of the steam was taken by a thermometer 
inserted in the main steam-pipe within a few feet of the boiler. 
This thermometer was broken, so that readings could not be 
taken during the second test. 

The barometer was an aneroid, placed in the engine-room. 

The quantity of water fed to the boiler was measured in 
the following manner: A barrel, holding about 150 gallons, was 
placed upon a tested platform-scale, and supplied with cold 
water from the Cochituate main, and also with condensed 
water from the reheaters and steam-cylinder jackets. During 
the second test the exhaust steam from the boiler feed-pump 
was condensed in a small barrel placed above the weighing 
barrel, into which it was drawn from time to time. 

After having been weighed the water was run into a large 
tub, from which the feed-pump drew its supply. The meas- 
urement of the feed-water was checked -by a Worthington 
water-meter placed between the feed-pump and the feed-water 
heater. 

To ascertain approximately the amount of water returned 
from the cylinder-jackets and reheaters the amount of cold 
water used was measured during the second test by a meter 
placed on the Cochituate supply. 

About seven hours after the beginning of the first test a 
small leak was discovered from a safety-valve on the boiler 
feed-pipe between the pump and the hot-water meter. After 
being discovered, the water leaking was caught and returned 
to the feed-pump tub. For a period of about fourteen hours 
the leakage was weighed, and the rate so determined was used 
to make a correction for the time before the leak was discov- 
ered. The total amount of this correction was 650 pounds. 

On the second test all pipe connections with feed-pipes^ 



TESTS OF SIMPLE AND COMPOUND ENGINES. 



297 



boilers, and engine, except those in use, were disconnected to 
avoid all chance of error from leakage. 

Temperatures of the feed-water were taken before and after 
passing through the feed-water heater by means of thermome- 
ters inserted in the feed-pipe. 

A thermometer in a tube partially filled with oil was in- 
serted in the flue to ascertain the temperature of the gases 
beyond the feed-water heater, and on the second test a similar 
thermometer was placed in the flue between the boiler and 
heater. 

Throughout the trials half-hourly observations were made 
of the engine-counter, pressure of steam at engine and boilers, 
vacuum in condenser in inches of mercury, height of water in 
boiler, height of water in tub holding feed-pump supply, water- 
meters on boiler feed-pipe and cold-water pipe, barometer, 
temperature of steam, temperature of gases in flue, and tem- 
perature of engine-room. Fifteen-minute readings were taken 
of the force-main and pump-well gauges, and readings of the 
feed-water thermometers every ten minutes. 

Temperatures of the external air and indicator-diagrams 
from the steam-cylinders were taken hourly. 

A large number of observers were employed, and care was 
taken to secure accuracy in all of the observations. The more 
important records were taken independently by assistants. 

No calorimeter tests were made to ascertain the quality of 
the steam. For the purposes of calculation it has been as- 
sumed that all of the water was evaporated into dry steam. 

Record of two Duty Tests of Engine No. 3 (Leavitt), at the 
Boston Main Drainage Works. 



1. Date of trials 

2. Time of beginning trial 

3. Duration 

4. Total revolutions 

5. Revolutions per minute 

6. Displacement of pumps per revolution ... 

7. Distance from o of gauge down to sewage 

in pump-well 



First Test. 



Mar 



24-25/85. 

10.06 A.M. 

24h. 43m. 

19,526 

i3-r7- 
226. 19 cu. ft. 

11.68 ft. 



Second Test. 
May 1-2, 1885. 

10.31 A.M. 

24h. 3|m. 

19.372 

13.42. 

226. 19 cu. ft, 

15.48 ft. 



298 



THERMODYNAMICS OF THE STEAM-ENGINE. 



9- 



11. 
12. 
13. 
14. 



17. 
18. 
19. 
20. 
21. 

22. 

23. 
24. 



25. 
26. 

27. 
28. 



[St trial 



Height of sewage in pipe-chamber, as 
given by mercurial gauge, graduated to 
give equivalent height of column of fresh 
water 

Pressure in force-main, near the pump, as 
indicated by column of fresh water at 
temperature 55° F 

Correction of mercurial gauge for friction 
in force-main, from data furnished by 
comparison of No. 8 and No. 9 

Total lift , , 

Weight of fresh water per cubic foot 

Total weight of dry coal consumed 

Duty of engine as developed by the trials: 
19526 X 226.19 X 37-8o X 62.42 _ 

2d trial ^9372 X 226.19 X 4243 X 62.40 _ 
94-78 

Mean pressure of steam in boilers 

Mean pressure of steam in main steam- 
pipe near engine 

Mean vacuum in condenser 

" atmospheric pressure by barometer. 
" temperature of air in engine-room. . 
" " of external air 

Total volume of sewage pumped by plun- 
ger displacement 

Total volume of sewage pumped, as actu 
ally measured 

Average slip of pumps 

Indicated horse-power, as determined by 
the measurement of two sets of cards for 
each trial 

Horse-power in sewage lifted, pump meas 
urement, no allowance for slip 

Work done by pump in per cent, of indi 
cated horse-power 

Coal burned per hour per indicated horse- 
power 

Steam per indicated horse-power per hour. 



First Test. 



25.76 ft. 



0.36 ft. 

37.80 ft. 

62.42 lbs. 

8,307 lbs. 



125,450,000'* 



99.4 lbs. 



28.1 in. 
30.18 in. 
67.5 deg. 
31.7 deg. 

33,038,000 gals. 

30, 224,000 gals. 
8.5 per cent.f 



251.5 H. P. 

'212.9 H. P. 

84.66 per cent. 

1.33 lbs. 
13-9 



Second Test. 



26.55 ft. 
26.95 ft. 



42.43 ft. 
62.40 lbs. 
9,478 lbs. 



122,400,000 
98.6 lbs. 

96. 1 lbs. 
28.0 in. 

29.81 in. 
75.2 deg. 
40.6 deg. 

32,778,000 gals. 

31,256,000 gals. 
4.6 per cent. 

290.2 H. P. 

243-5 H. P. 

83.90 per cent. 

1.35 lbs. 
14.2 



* To reduce this duty on the first trial to the usual standard, it is necessary to make a cor- 
rection for the coal used to supply steam to the feed-pumps. Assuming the duty of the feed- 
pump to be 10,000,000, the corrected duty of the pumping-eng^ine is 122,500,000. 

t At the end of the first test it was found that two of the rubber discharge-valves had been 
torn oflE, which accounts for the large slip. A study of the question indicated that this would 
not materially affect the duty, a view which is corroborated by the uniform relation between 
the indicated and the actual horse-power in the two tests. The loss of action in the pumps, 
when the valves were less worn, was about 2.5 per cent. 



TESTS OF SIMPLE AND COMPOUND ENGINES. 



299 



Record of two Tests of Boiler No. 2, at the Boston Main Drainage 
Works, made in Connection with Engine Tests. 



3- 

3«. 
4. 

5. 

6. 



II. 
13. 
14- 

14a. 

15- 
153. 



18. 
19. 
20, 

21. 
22. 

26. 

26a. 

2bb. 
2tc. 



Date of trial 

Time of beginning trial. 
Duration of trial 



Dimensions and Proportions. 
The general description of the boiler is 

given in Mr. Leavitt's paper. 

Grate surface 

Area of least draught 

Water-heating surface . . . 

Super-heating surface 

Heating surface in feed- water heater 

Ratio of water-heating surface to grate 

surface 



Average Pressures. 

Steam-pressure in boiler by gauge 

Absolute steam-pressure 

Atmospheric pressure by barometer 

Average Temperatures. 

Of external air 

Of steam 

Of escaping gases before passing feed- 
water heater 

Of escaping gases after passing feed-water 
heater 

Of feed-water before passing heater 

Of feed-water after passing heater 

Of Cochituate water 



Fuel. 



Dry coal consumed 

^ , , , J ^ ist test, 432 lbs 

Total refuse dry •] ^, ,. ' ^;^^ ., 

^ / 2d 497 

Total combustible (weight of coal, item 18, 

less refuse, item 19) 

Dry coal consumed per hour 

Combustible consumed per hour 



Water. 
Total weight of water pumped into boiler 

and apparently evaporated 

Check on above measurement by meter 

measurement 

Per cent less by meter 

Feed-water taken from Cochituate main, 

meter measurement 



First Test. 



Mar. 24-25, '85 
9.58 A.M 
24h. 51m. 



ft, 



45.5 sq. 

5-50 " 

1,826. " 

6. " 

934- " 



40-1 

99.4 lbs. 
114. 2 " 
30.18 in. 

31.7 deg. 
339-0 " 



183.5 deg, 

96.5 deg, 

145. 1 deg, 

38 deg. 



8,307 lbs. 
5.2 per cent. 



7,875 lbs. 
334-3 lbs. 
316.9 lbs. 



86,783 lbs. 

85,629 lbs. 
1.3 per cent. 



Second Test. 



May 1-2, 1885. 
10.25 A.M. 

- 24h. 9^m. 



45. 


5sq 


ft. 


5 -50 






1,826. 


(< 


*« 


6. 


" 


" 


934. 


" 


" 



40-1 

98.6 lbs. 
113. 2 " 
29.81 in. 

40.6 deg. 



439 deg. 

194.2 deg. 

120.7 deg. 

164. 1 deg. 

46 deg. 



9.478 lbs. 
5.2 per cent. 



8,981 lbs. 
392.3 lbs. 
371.8 lbs. 



98,780 lbs. 

96,622 lbs. 
2.2 per cent. 

78,836 lbs. 



300 



THERMODYNAMICS OF THE STEAM-ENGINE, 



28. 



29. 



30. 



31. 



32. 



33. 



34. 



Economic Evaporation. 
Water actually evaporated per pound of 
dry coal, from actual pressure and tem 

perature 

Equivalent water evaporated per pound of 
dry coal from and at 212° F. : 

Including f.w.h 

Excluding f.w.h 

Equivalent water evaporated per pound of 
combustible from and at 212° F.: 

Including f.w.h 

Excluding f.w.h 



Commercial Evaporation. 

Equivalent water evaporated per pound of 

dry coal, with one sixth refuse, at 70 lbs. 

gauge-pressure, from temperature of 

100° F. = item 33 multiplied by 0.7249: 

Including f.w.h 

Excluding f.w.h 



Rate of Combustion. 
Dry coal actually burned per square foot 
of grate surface per hour 

Rate of Evaporation. 
Water evaporated from and at 212° F. ; 
per sq. ft. of heating surface per hour, 
excluding f.w.h 

Commercial Horse-power. 
On the basis of 30 lbs. of water per hour 
evaporated from temperature of 100° F. 
into steam of 70 lbs. gauge-pressure 
( = 34^^ lbs. from and at 212°): 

Including f.w.h 

Excluding f.w.h 



First Test. 



10.45 lbs, 



12.12 lbs. 
11.60 lbs. 



12.78 lbs. 
12.23 lbs. 



9.26 lbs. 
8.87 lbs. 



7.35 lbs, 



2.12 lbs. 



117 H. P. 
112 H. P. 



Second Test. 



10.42 lbs. 



11.83 lbs. 
11.35 lbs. 



12.48 lbs. 
11.98 lbs. 



9.05 lbs. 
8.68 lbs. 



8.62 lbs. 



2.44 lbs. 



134 H. P. 
129 H. P. 



CHAPTER XVII. 

HIRN'S ANALYSIS. 

The best insight into the actual behavior of steam in the 
cyhnder of an engine is given by Hirn's analysis, and tests giv- 
ing sufficient data for such an analysis are of special interest 
and importance, since they indicate why one method of run- 
ning an engine gives a better result than another. 

Hirn* gives the data and the analysis of four such tests^ 
made on engines with and without a steam-jacket, and using 
moist or superheated steam, which will not be quoted here^ 
since the same ground is covered by later experiments made 
under his direction or inspiration. 

The most notable tests, recorded in Tables XII to XV, are 
given by Hallauer.f Many of the tests were made by him 
personally, and all were worked up by him from the original 
data. 

Hallauer's Tests on Simple Engines. — In Table XII are 
given the data of tests made on an engine designed by Hirn 
to use superheated steam. It had four independent flat valves 
moved by cams. These are all the tests given by Hallauer in 
which the complete data are given ; in all other tests some of 
the data are missing, and the results and conclusions, only, are 
given here. 

In Table XII are given the results of these tests and of tests 
made on an engine of the Corliss type with a steam-jacket. 

Though it is not so stated in Hallauer's memoires, it ap- 
pears that during these tests these engines were coupled with 
another engine, and that the speed was controlled by that en- 
gine, with the intention that the point of cut-off and the work 
of the engine should remain constant during a test. The same 

* Th6orie mecanique de la chaleur. 1876. 

f Bulletin de la Soc. ind. de Mulhouse, vols, xlvii.-liii. ; 1877-1883. 

301 



302 THERMODYNAMICS OF THE STEAM-ENGINE. 

method seems to have been employed during most of the tests 
of compound engines given in Table XIV. 

Observations Taken. — (i) The steam consumed was deter- 
mined by measuring the feed-water in a tank alternately filled 
and emptied. The level of the water in the boiler was noted 
evening and morning, and allowance made for the difference ; 
also, the absence of leaks was made certain by applying hydrau- 
lic pressure to the boiler, pipes, and so forth. 

(2) The water rejected by the air-pump was gauged by al- 
lowing it to flow through an orifice in a copper plate under 
considerable head. The flow through the orifice used was de- 
termined by direct experiment under the conditions which ob- 
tained during the experiment. 

(3) The superheating, when it occurred, was measured di- 
rectly by a good mercurial thermometer placed in a tube let 
into the steam-pipe near the engine-cylinder. 

(4) The per cent of water mixed with the steam, when satu- 
rated steam was used, was determined by calorimetric experi- 
ments. In some cases this quantity appears to have been in- 
ferred from experiments made at other times under similar 
conditions. 

(5) The rise of temperature of the injection-water in Hal- 
lauer's own work was determined by a differential air ther- 
mometer reading to one fiftieth of a degree Centigrade. 

(6) Other temperatures were taken with mercurial ther- 
mometers, or were deduced from the indicated pressures, by 
aid of tables of the properties of steam. 

(7) The work was measured by aid of a good steam-engine 
indicator, and in some cases by Hirn's flexion pandynamome- 
ter, which utilized the beam of the engine as a spring for meas- 
uring the force exerted by the steam on the piston. As before 
indicated, the diagrams thus obtained also gave the pressures 
at the several interesting points of the stroke, from which the 
temperatures were determined. 

(8) The revolutions per minute, steam-pressure, and other 
required observations, were taken by aid of proper instruments. 



BIRN'S ANALYSIS, 303 

The greater part of Tables XII and XIII is sufficiently in- 
telligible from the preceding account of the observations 
taken, and from the headings of the columns. The following 
explanation will make the rest clear : 

The real cut-off given in column 5 of both tables is the 
ratio of the volume of steam in the cyHnder at cut-off to the 
volume at the end of the stroke ; it is therefore the reciprocal 
of the number of expansions. 

In Table I, the absolute pressures, in columns 11-18, were 
measured on the indicator-cards, and the temperatures corre- 
sponding were taken from tables of the properties of steam. 

The works in the same table were obtained by measuring 
the appropriate areas on the indicator-card with the polar 
planimeter. The corresponding quantities of heat were ob- 
tained by dividing by 424. 

In Table XIII, column 9, the net horse-power for experi- 
ments 9-1 1 is deduced by comparison with other experiments, 
for which the power was measured by a brake. 

In the same table, column 10 shows that the work required 
to expel the steam from the cylinder varies widely, as com- 
pared with the total absolute work during the forward stroke. 
This is due in part to the varying power of the forward stroke, 
and in part to the variation in the vacuum maintained in the 
condenser. To make proper comparisons of different engines, 
the back pressure should be the same in all, or, as that is sel- 
dom possible, they should be reduced to a common back pres- 
sure. The simplest and the customary reduction is to assume 
that the back pressure is zero, or that the vacuum is perfect. 

The assumption just made gives rise to a term called total 
or absolute horse-power, i.e., the horse-power the engine would 
have if it exhausted into a perfect vacuum, and usually, if 
there were no compression. 

The consumption of dry saturated steam, columns 11-13, is 
deduced from the actual consumption of superheated or moist 
steam, by multiplying by the heat required to raise one pound 
of water from freezing-point to the pressure and condition 



304 THERMODYNAMICS OF THE STEAM-ENGINE, 

stated, and then dividing by the total heat of saturated steam 
at the same pressure. In two cases the steam for total horse- 
power is the actual weight of superheated steam, and for the 
same experiments the consumption per net horse-power is not 
given. Again, the net horse-power is not stated for any of the 
experiments on the Hirn engine. These several inconsisten- 
cies, and others, found in these tables and in Tables XIV and 
XV, are due to the fact that they are condensed from calcula- 
tions and tables given by Hallauer in several different me- 
moires, which, being for specific purposes, included such of the 
experiments as were convenient. As the details of some of 
the calculations are not explicitly stated, I have not thought 
it profitable to supply the omissions. 

In the work of Hirn and Hallauer, the heat Q^, rejected 
from the walls of the cylinder during exhaust to the condenser, 
receives special attention, and is the only one of the several 
quantities (2a j Qb', Qc arid Q^, which is directly calculated by 
them. Hallauer's calculations are, however, in such form that 
the other quantities may be easily deduced from them with 
good degree of approximation. In Table III have stated the 
quantities Q^ and Qj, thus obtained ; Q^ is not regarded, as the 
compression was very slight. For the same reason, and be- 
cause the engines usually had a good vacuum in the condenser^ 
the weight M^ is neglected. 

In Experiment 8, when the condenser was not used, and 
where the steam was strongly superheated and much wire- 
drawn by throttling, the heat rejected to the condenser be- 
comes — 1.2 per cent, a result which is impossible. In this 
test the condenser was not used, and no check on this quan- 
tity could be made. This discrepancy may be due to the 
fact that the steam was superheated throughout its passage 
through the engine ; or it may be the error of the test. 

Hallauer's Method of Calculation. — To show this method 
and compare it with the theory developed on page 185, an 
example will be given, using the test on the Hirn engine made 
Sept. 7, 1875. This test, with some others on the same en- 



HIRN'S ANALYSIS. 



305 



TABLE XII. 
Data of Tests on Hirn Engine. 













i 


iL 


§,.• 




Date. 


Condition. 


03 

c 

.2*; 

a 3 
o.S 


3° 




c V-.2 


ipi 








Sa 


1% 


^ ^'-S 


.i^'-= « 


^atS 










»;^ 


^ 


^ 


^ 


1. 


2. 


3. 


4. 


5. 


6. 


7. 


8. 


1 


Nov. 18. 1873 


Superheated, 230° 


30.1736 


0.2570 


0.3065 


9-3500 




2 


Nov. 28. 1873 


Saturated, 


30-5494 


0.2570 


0.3732 


9 


29175 


0.0037 


8 


Aug-. 26, 1875 


Superheated, 215° 


29.969 


0.2139 


0.2651 


8 


7291 




4 


Au^. 27, 1875 


Superheated, 223° 


30.306 


0.4539 


0.2822 


8 


59^3 







Sept. 7, 1875 


Superheated, 195° 


29.98 


0.1628 


0.2240 


8 


73«4 




6 


Sept. 8. 187s 


Saturated, 


30-41 


0.1628 


0.2634 


8 


9132 


0.0030 


7 


Sept. 29, 1875 


Superheated, 220° 


30-13 


0.4539 


0.2265 


5 


9810 




8 


Oct. 28, 1875 


Superheated, 220° 


30.00 


0.2867 


0.2714 











Absolute pressures in kilos per sq. 


m., and corresponding tempera- 




Temperatures of 
injection-water. 


tures of saturated steam in degrees C. 
















Boiler. 


Cut-off. 


Release. 


Back pressure. 




Initial. 


Final. 


Pres- 
sure. 


Temp. 


Pres- 
sure. 


Temp. 


Pres- 
sure, 


Temp. 


Pres- 
sure. 


Temp. 




9. 


10. 


11. 


12. 


13. 


14. 


15. 


16. 


17. 


18. 


1 


12.6 


31-3 


48900 


150.15 


42449 


144.96 


9355 


97.24 


3680 


73-49 


2 


11.83 


33-65 


46380 


148.20 


37773 


140.78 


9701 


98.24 


3670 


73-42 


3 


16.50 


33-09 


49938 


151.00 


41415 


148 74 


7722 


92.05 


1919 


58.86 


4 


16.50 


35.26 


48075 


150.00 


23070 


124.00 


8417 


94-40 


1900 


58.25 


5 


16.37 


30.42 


49680 


150.77 


39128 


142.00 


5931 


85.00 


1881 


58.44 


6 


16.50 


32.25 


49706 


150.77 


38339 


141-30 


5737 


84-33 


2134 


61.15 


7 


15.85 


37-81 


50255 


152.20 


17458 


115.80 


6457 


87-36 


1759 


57-" 


8 


^~~* 




43754 


146.20 


34333 


137-40 


11053 


101.89 











Work in meter-kilograms and corresponding heat in 


calories. 










At full pressure. 


Of expansion. 


Of back 


press're 


Total, absol'te 


Real, indicated. 


1' 




Work. 


Heat. 


Work. 


Heat. 


Work. 


Heat. 


Work. 


Heat. 


Work. 


Heat. 






19. 


20. 


21. 


22. 


23. 


24. 


25. 


26. 


27. 


28. 


1 


1 


5531-5 


13.01 


7020.5 


16.52 


1787.0 


4.205 


12552 


29-53 


10765 


25-325 




2 


5103.5 


12.005 


6725-5 


15-835 


1782.5 


4.19 


"833 


27.84 


10050 


23 


65 


JJ 


3 


4415-0 


10.39 


6710.0 


15 


79 


932.0 


2.19 


11125 


26.18 


10193 


23 


Q9 




4 


6285.0 


14.79 


3930 


9 


24 


922.0 


2.17 


102 1 5 


24.03 


9293 


21 


86 


^ 





3315.0 


7.80 


6085.0 


14 


31 


9x2.0 


2.14 


9480 


22. n 


8487 


19 


97 




6 


3-87.0 


7-50 


5825.0 


13 


70 


1035.0 


2.43 


yoi2 


21.20 


7977 


18 


77 




7 


5225.0 


12.29 


3070.0 


7 


22 


862 


2.02 


8295 


19-51 


7433 


17 


49 


)i 


8 


5000.0 


11.76 


6162.0 


14.50 


5212.0 


12.26 


11162 


26.26 


5950 


14.00 


Oi 



3o6 



THERMODYNAMICS OF THE STEAM-ENGINE, 



TABLE XIII. 
Results of Experiments on Simple Expansive Engines. 



















v^ 










« 


S • 


Absolute 


Horse- 


3 










p 


£ 


pressures in 


power. 
Cheval k 












_a."M 


kilos, per 


Kfl 




Name 






s 


^a 


square 


vapeur. 


m2 




of 
Engine. 


Date. 


Condition. 


S. 


« 






.2° 








s 
.2 


r. 




t 


•d 




Ji G 










3 
"o 


g^ 


<u 


M ^ 






1^ 










% 


S^o 


'0 


^a 


•0 




s.s 










C4 


p^ 


CQ 


03 




^ 


!^ 




1. 


2. 


3. 


4. 


5. 


6. 


7. 


8. 


9. 


10. 


1 


Hirn 


Nov. i8, 1873 


Superheated, 231° 


30.1736 


0.2570 


48900 


3680 


144.36 




8-3 


2 


" 


Nov. 28, 1873 


Saturated 


30.5494 


0.2570 


46380 


3670 


136 


46 






8 


8 




Aug. 26, 1875 


Superheated, 215° 


29.969 


0.2139 


49938 


1919 


I3S 


77 




b 


4 


4 


" 


Aug. 27, 1875 


*Superheated, 223° 


30.306 


0.4539 


4807 s 




125 


17 


114. 


8 


9 


4> 


" 


Sept. 7, 1875 


Superheated, 195° 


29.98 


0.1628 


49680 


i88r 


113 


08 


102.0 





7 


« 


" 


Sept. 8, 1875 


Saturated 


30.41 


0.1628 


49706 


2134 


107 


81 


95-0 


II 


8 


7 


" 


Sept. 29, 1875 


t Superheated, 220° 


30-13 


0.4539 


50255 


1759 


00 


53 




10 


4 


« 




Oct. 28, 1875 


$ Superheated, 220° 


30.00 


0.2867 


43754 




78 


30 




4b 


7 


9 


Corliss 


1878 


Saturated, jacketed 


50.41 


tV 




1480 


105 


92 


10 





10 


" 


1878 


Saturated, jacketed 


51.12 


^ 




1690 


137 


125 


8 


8 


11 




1878 


Saturated, jacketed 


49-34 


i 




1840 


158 


142 


8.1 



* Throttle-valve partly closed. t Valve nearly closed. X Non-condensing. 





Consumption of equiv- 
alent dry saturated 
steam per horse-power 
per hour, kilos. 


Per cent of water 

in mixture in the 

cylinder. 


Exchange of heat in per cent of total heat 
furnished per stroke. 




i 

2 & 




1 


! 
3 

u 


rt 
<u 

< 


^; 


•030 
tu-a'S 

111 


si 




c 
.2 
Pi 




-^ a 


3 w 

|| 

rt'rt 
3 w 

y.S 
< 




PU 


(1h 


i 








Oa 


Q, 


Qc 


Qe 


Qi 


^. 


Qc 




11. 


12. 


13. 


14. 


15. 


16. 


17. 


18. 


19. 


20. 


21. 


22. 


23. 


1 


7.000 


7-633 


8.207 


6.50 


12.00 


4-9 


II. 


2.0 


7-8 


1.2 




-0.40 


16.61 


2 


8,449 


9 


307 


10.341 


30.40 


25.20 


9-4 


23-9 


7-3 


15-4 


I.O 




0.25 


37-53 


8 


6-7519 


7 


3691 




0.38 


17-50 


7-9 






9-7 


1-4 




3-2 


17.60 


4 


7.874 


8 


6SS 


95" 


T — T.50 


13.20 


3-11 






10.5 


1-3 




0.30 


^°-34 


b 


6.655 


7 


370 


8.188 


24.64 


21.38 


8.10 


22.4 


8.4 


12.5 


1.6 




0.05 


18.80 





7.822 


8 


837 


9.929 


36.00 


35-19 


10.63 


28.3 


5-0 


21.6 


^•5 




—0.20 


37.02 


'4 


7-763 


8 


663 


9 844 


2.52 


15-85 


1. 10 






14.2 


1.6 




3-20 


21.90 


8 


*6.562 


12 


31 S 




12.00 


Dry. 


Dry. 






— 1.2 








-1.84 


9 


7.188 


7 


083 


9.071 


38.30 


21.70 




26.4 


17-5 


12.3 


1.65 


5-1 


1.9 


II. 21 


10 


7.236 


7 


039 


8.724 


31.70 


19.20 




21. 1 


15.0 


9.8 


1-3 


4-9 


1.2 


II. 14 


11 


7-307 


7-955 


8.646 


25.30 


18.50 


.... 


15-4 


10.4 


8.0 


I.I 


4.1 


I.I 


II. 15 



= Superheated steam per horse-power per hour. t Superheated. 



IIIRN'S A ANALYSIS. 3O7 

gine, is calculated twice, in a memoir presented in 1877, and 
again in one presented in 1878. There are some differences 
in the two methods, and some of the others show discrepancies 
that do not appear to be readily explained. In the tables 
given I have adhered to the earlier calculation, where the 
entire data are given. 

CALCULATION OF TEST ON HIRN ENGINE, Sept. 7, 1875. 

Volume of cylinder, including clearance at one end, 0.490 cu. m. 

Specific heat of superheated steam, <r^ = 0.5 

Calories- 
Heat brought by dry vapor in cylinder, 0.224 (606.5 +0-305 X 150-77) = 146.15 
Heat brought by superheat, 0.5 X 0.224 (i95«5 — 150-77) = 5-oi 



Total heat brought to cylinder, 151. 16 

Heat carried away by condensed water, 0.224 X 30.42 = 6.81 



Difference, available heat, 144-35 

Heat absorbed by condensing water, 8.7384(30.42 — 16.37) = 122.77 



Difference, 21.58 

Heat equivalent of external indicated work, 19-97 

Heat lost by radiation, etc., 2.5 22.47 



— 0.89 

Per cent of error, '— ■=. — o$^.6. 

151. 16 

The consumption of dry saturated steam per stroke, calculated from the 

151. 16 , 

total heat, is -^ = o.*2<?i7. 

652.48 

T-L - J- J 1. . 2 X §487 X 29.98 

The mdicated horse-power is —^— = 113.08. 

^ 60 X 75 

The net horse-power is 113.08 X 0.90 = 102. 

The consumption of dry saturated steam per horse-power per hour is : 

»r . , U 0.2317 X 60 X 60 X 75 . yr 

Total horse-power, — ^—!- — — 6.*655 ; 

9400 

. ^. , , 0.2317 X 60 X 60 X 75 . 

indicated horse-power, — ^—^ — — = 7.^370 ; 

7 370 
net horse-power, = 8.*i88. 

0.90 



308 THERMODYNAMICS OF THE STEAM-ENGINE. 

Weight of mixture of steam and water in the cylinder, 0^.2240 

Weight of dry steam at cut-off, 0.1628 X 0.490 X 2. 116 = 0.1688 



Weight of steam condensed during admission, = 0.0552 = 24^.6 

Heat yielded during condensation, 0.0552 X 506.5 = 27'^. 96 

Weight of dry steam at end of stroke, 0.490 X 0.3595 = 0^1761 

Weight of water in mixture, = 0,0479 = 21^.38: 

Internal heat at cut-off, 0.1688 X 462.68 -f- 0.224 X 143.26 = 110.22: 

Internal heat at end of stroke, 0.1761 X 507.77 + 0.224 X 85.32 = 108.56 

Difference, 
Heat furnished by superheat, (i95-5 — 142)0. 

Heat furnished by condensation during admission, 





1.66 


0.224 = 


5-99 




27.96 




35.61 


14.31 




2.50 


1681 



Sum, 
Heat absorbed by work of expansion, 
Heat lost by radiation, etc., 

Qc, the heat rejected by the walls to the condenser, = 18.80 

18 80 
In per cent of total heat received, Qc = — '—- = 12^.5. 

151. 16 

Internal heat at the end of the stroke, I08'^.56 

Heat equivalent of work of back pressure, 2,14 

Heat carried away by condensed water, — 6.8r 



103.89 
Heat acquired by condensing water, 122.77 

Difference Qc, = 18. 88- 

r- . J , . ,. , ^ 18.88 — 18.80 

Error m determmation of Qc = =r 05^.0"i. 

151. 16. ^ ^ 

Heat yielded by 0^.224 dry steam in condensing, 

0.224 (624.32 — 30.42) = 133^.03 
Heat acquired by condensing water, = 122.77 



10.26 



TTT • 1 i? . , 10.26 ^ o.oiSm 

Weight of water contamed -— = o^^.oiSig = ~ = 85^.1. 

565.75 0.224 

From the quantities already calculated, the two remaining quantities Qa and 
Qb may be found ; Qd is considered to be zero. 

Heat furnished by condensation during admission, 27*^.96 

Heat furnished by superheat, 5;. go 

Q»> = 33.95 



HIRN'S ANALYSIS. 309 

Heat equivalent of work of expansion, 14 31 

Internal heat at cut-off minus internal heat at end of stroke, 1.66 



Qb = 12.65 

151. 6 

Hallauer's Tests on Compound Engines. — Table XIV 
gives the results of experiments made on stationary compound 
engines of different types. Experiments 1-7 were made on a 
vertical Woolf beam engine working at Munster. It had the 
two cylinders side by side acting on the same end of the beam, 
the small cylinder nearer the columns so that it had a shorter 
stroke. Both cylinders were jacketed with steam brought 
from the boiler in a special pipe. The engine was normally 
controlled by a throttle governor, but during the experiments 
the governor was disconnected, and the engine was run coupled 
with another engine which controlled the speed. Experiments 
8 and 9 were made on a horizontal Woolf engine having the 
small cylinder above the large one, and inclined at a small 
angle, so that both pistons acted on one crank. Both cylin- 
ders were jacketed with the steam passing from the boiler to 
the small cylinder — a method that cannot be recommended, 
since the condensation in the jacket makes the steam moist as 
it enters the cylinder. Experiments 10-13 were made on a 
double vertical Woolf engine coupled to the same shaft ; 10 
and 12 were made on the left engine, and ii and 13 were 
made on the right engine. The engine was controlled by a 
governor which varied the cut-off of the small cylinder. The 
cylinders were jacketed with the steam passing to the small 
cylinders. Experiment 14 was made on a vertical Woolf beam 
engine, working at Saint-Remy. 

Tests on Marine Engines. — Table XV gives the results 
of experiments on various marine engines. Since the weight 
of the circulating water could not be determined, the check on 
the calculation of Q, could not be obtained. 

Experiments i, 4, and 5 are entered twice in the table, — the 
first time as calculated with the data given by the experiments, 
and the second time with modified data which give more con- 



310 



THERMODYNAMICS OF THE STEAM-ENGINE. 



TABLE XIV. 
Results of Experiments on Stationary Compound Engines. 















Absolute 




C 










S 




pressures. 


Horse- 


oi-S 










? 





kilos. 


power. 


i; 




Place. 


Date. 


Dimen- 
sions. 


a 


c 

2. 


per sq. m. 








i^ 






l.s 










.1 



.2 






TJ 




11 












<A 




'^se 


rt 




u 

I- 












> 


^ 


4» 
1 


1^ 


"■5 


4; 


1 


Munster. 


Sept. 21, 22, 1876 


High-pres- 


25-3 








180.23 




22.92 


2 


" 


June 20, 21, 1876 


sure, diam. 


25.0 




51670 




246 


02 






3 


" 


Oct. 24, 25, 1876 


o^.ss, stroke 


2S.6 








284 


28 


.... 


.... 


4 




Oct. 17, 18, 1876 


i'°.4i5. Low- 


25.1 









346 


39 





19. 6& 


5 


" 


June 12, 13, 1877 


pressure, 


25-4 




42369 




185 


75 


.... 


24.10 


« 


" 


June 21, 22, 1877 


diam. i™.2oo 


25.2 


.... 


51670 




267 


8s 


.... 


20.52 


1 


" 


July 4, 5, 1877 


stroke 2™. 00, 


25-25 





S68,7 


2930 


347 


16 




17-43 


8 


( Factory, 
\ DoUfus, 
( Mieg&Cie 


Nov., 1876 


Diameier, 
h. p. o'°.38i, 


39-37 


6 


49600 


2530 


130 


112.08 


20.06 


9 




1. p. on».8575, 
stroke, 1.297 


39-37 


6 


38380 


2950 


181 


161.00 


.... 


10 


Malmer- 


1877 




26.2 


28 


56837 


I8I0 


143.11 


118.38 


18.6 


11 


spach. 




25-93 


25 


56837 


1750 


149-53 


124.74 


17-5 


12 


" 






25-47 


13 


58903 


2260 


215.7 


185.69 


15 -f> 


13 


" 


•' 




24-83 


13 


58903 


2180 


212.92 


183.67 


14.9 


14 


Saint-Remy 





Ratio cyls. 


24-503 


19 


32220 


.... 


137.00 


107.88 


9-9 


15 


Woolf* 


.... 


0.147 


25 


0.131 




2690 


367 





15-7 


1« 


" 




0.147 


25 


0.131 




1760 


178 




20.0 


17 


" 


.... 


0.182 


25-S 


0.0778 




2150 


220 





14.7 


IS 


"■ 




0.182 


26.0 


0.0385 




1730 


150 




17.0 


19 


Compound. 


.... 


0.348 


88.5 


0.132 






78.5 




17.6 



Kind of engine. 





Consumption of 


equiv- 


Per cent of water. 


Exchange of heat in per cent of total 
heat per stroke. 




alent dry saturated 






' 














steam per horse 


power 






y 




bfi 














per 


hour, kilos. 


a 


bJDu 


a 


4-. (U 

i% 


5 

"-a 


c 

11 
a 

< 


% 




c 


H 

.s a 


1 


X) 

■s . 

n 


.S 

3 




% 
° Y. 


?iS 


H 










% 






i\ 


G 


■hi 


to 


1% 


3-r-i 


3-3 




H 




^5 


Oh 


<1 


< 


U 


Qa 


Qc 


Qi 


Qe 


Qj 


Qc 


1 


7-6605 


9-9399 





5-5 


16.61 


30.97 


12.52 


8.36 


6.20 


0.24 


1.83 


8.12 


23-74- 


2 


7-7434 


9 


5619 









16.29 


32.06 


10.32 


8 


54 


5-90 


0.25 


1.3b 


6.63 


30.27 


3 


7.3966 


9 


3984 










12.09 


31.68 


13-75 


5 


25 


6.65 


0.43 


1.23 


6.21 


38.10. 


4 


7.6104 


9 


4663 









16.00 


30.43 


12.33 


7 


43 


5-45 


1.26 


0.98 


6.25 


38-94- 





7-3841 


9 


7299 


12. 411 




35 


21.17 


32.18 


7-39 


14 


44 


3-50 


3-5 


1. 81 


8.. 37 


13-48 


6 


6.9452 


8 


7390 


10.357 






14.21 


28.44 


5-39 


8 


58 


1.32 


1.32 


1.38 


7.24 


6.65 


7 


7.1121 


8 


6140 


9.864 




8 


16.17 


28.90 


6.60 


10 


12 


3..38 


3-38 


1.08 


6.80 


21.8^ 


8 


7.290 


9 


l2o 


10.563 







11.20 




5-34 


6 


43 


1. 19 


O.IO 


2.14 


8.05 


1-95 


9 


7.328 


8 


878 


9-975 







10.8 




4-50 


5 


56 


0.75 


0.45 


I-S9 


6.15 


1. 16 


10 


6.731 


8 


273 


10.019 







40.0 


.... 


17.60 


25 


5 


7-8 


1.6 


1.9 


6.7 


19.34- 


11 


6. 821 


8 


260 


9.898 







36.1 





17.80 


22 


7 


8.2 


0.9 


1.8 


6.7 


21-33 


12 


6.878 


8 


149 


9-465 







23-7 




17.90 


13 


72 


8.40 


3-7 


1.23 


5-94 


31-4+ 


13 


6.983 


8 


210 


9-517 







24.7 




19-5 


14 


43 


9.90 


1.6 


1.20 


5-96 


37.80. 


14 


6.840 


7 


591 


9.702 







— 


— 




.. 














lb 


7.042 


8 


354 








9-4 


•■•8.9 


9-9 






4-9 


0.7 


.... 




33-1 


10 


7-316 


Q 


145 








10.8 


10.4 


X0.6 






6.4 


0.2 


.... 




22.9 


17 


6.883 


8 


o6q 








23-2 


10.4 


17.8 






10.2 


0.8 


.... 




38.Q 


18 


6.831 


8 


228 








39-0 


20.1 


16.4 






9-3 


0.4 







24-3 


19 


6.667 


7 


376 








29-7 


15.2 


15-9 






4-5 


0.8 






1.6 



* Per cent of water at end of stroke, small cylinder for 15-18. 



HIRN'S ANAL YSIS. 3 1 1 

sistent results. In Experiment i, the steam at cut-off in the 
small cylinder appears to have 0.2 per cent of water, and at the 
end of it appears to be dry. Hallauer thinks this improbable 
even with an efficient steam-jacket, since the steam passages 
and valve openings are large, so he gives a recalculation in \a 
which augments the consumption by the amount cf 

8.416 — 8.170 

^ — -^ — — = 2.8 per cent. 
8.416 ^ 

In like manner. Experiment 4 appears to give dry steam at 
cut-off of the small cylinder, and superheated steam at the end 
of the stroke. The modified results of 4a show augmentation 
of consumption of 3.5 per cent. From analogy the next ex- 
periment has the consumption increased by 1.8 per cent in the 
second form, ^a. 

To me, such a change of the original data appears to be 
questionable, and the modified results are certainly in doubt to 
an extent equal to the modification made. I have given the 
original data the preference in the table, but have included the 
modified results which are used by Hallauer in his compari- 
sons with other engine tests. 

Discussion of Results. — The experiments recorded in 
Table XIII show clearly the effect of superheated steam, and 
of a steam-jacket on the interchange of heat between the 
steam in an engine-cylinder and the walls of the cylinder ; and 
show the reason of the economy resulting from these methods 
of using steam. 

When superheated steam is used, the heat Q^ absorbed by 
the cylinder during admission of steam is furnished in part by 
the superheat, and consequently there is less initial condensa- 
tion than when saturated steam is used. At release there is 
less moisture to be evaporated from the walls of the cylinder, 
which in turn reduces the amount of Q^. This is clearly seen 
from a comparison of Experiments i and 2, and 5 and 6, on tlie 
Hirn engine. The effect on the value of Q^, returned by the 
walls of the cylinder to the steam, is not so well marked. 
With the cut-off at ^ stroke (Experiments i and 2), the use of 



312 



THERMODYNAMICS OF THE STEAM-ENGINE. 



TABLE XV. 
Experiments on Compound Marine Engines. 





Name. 


Condition. 


Expansion. 


3 3 


J5 


13 
as 

^ c 

•^ U 


^n 








c 


il 


.2 

Is 








.2£ 


aj 5J 


f>2 


o.S 


il 




5;? a 








^ 


^ 


oi 


Pi 




^ 


n 


1 

2 
3 


Duquesne 


j Throttle open, long cut- 
1 off 

Throttle closed partly 
Throttle closed further 


0.519 


0.725 


0.376 


80.83 


8490 


13-^5 


2880 




<( 


11 


'• 


59-33 
44-49 


3180 
1410 


21.5 


1590 


4 

4« 
5 

ha 
6 




Cut-off shortened 


" 


0.650 


0.321 


76.^67 


7200 








Cut-off shortened 


tt 


0.550 


0.285 


73.00 


6360 


II. I 


2000 




Cut-off shortened 


" 


0.225 


0.126 


62.49 


3900 


17.7 


2460 


7 


" 


Cut-off shortened 


" 


0. 100 


0.052 


46.55 


166:; 


22.0 


1840 


8 


Vienne 


Receiver 


0.317 


0.660 


0.209 


75.00 


690 


13-4 


2160 


9 


Cigale 


Receiver 


0.309 


0.750 


0.232 


90.00 


205 


7-5 


1780 


10 


Nievre 


Three cylinders 


0.380 


0.499 


0.189 


93.80 


740 


11.3 


2420 


11 


Mytho 


" 


0.282 


0.601 


0.169 


44-48 


590 


16.4 


1070 


12 


" 


*' 


" 


" 


" 


61.40 


1350 


II. 2 


1150 


13 


" 


" 


" 


0.690 


0.194 


73- lb 


2200 


13-0 


1890 


11 


" 


" 




0.750 


0.212 


66.00 


2590 


I0.2 


1870 


16 


.... 


Receiver 


*o.8« 
1.45X0.9 


.... 




75-00 


68963 


.... 







Consumption of 


Per cent of water 


in the 


Exchange of heat in per 


cent of 




equivalent dry satu- 




cylinder. 




total heat 


per stroke. 




rated steam per 


















horse-power per 












ni 


OS 




hour, kilos. 


Bu 
ir. (U 

-•a 




U 


2 « 

il 




1 

•^ a 










> u 




"5 


.3 

-a 


3 " 






■is 


3.0 




•S.S 




H 




U 


w 


W 


Qc 


<2j 


Qe 


< 


1 


8.179 


9-405 


0.2 


dry 


7-1 


0.50 


1-57 


1.23 


27 


la 


8.416 


9 


678 


2.4 


2.2 


9-3 


1.05 


1-53 


1.20 


103 


2 


8.744 


10 


571 


7.2 


3 


8 


12.7 


5-75 


4-05 


1-93 


176 


3 


8.832 


II 


242 


4.0 


2 


7 


11. 


3-7 


4-7 


3-1 


7? 


4 


8. 114 


9 


394 


0.0 


s. 


h. 


8.6 


2.9 


2.9 


1.4 


138 


4« 


8. 411 




737 


3-4 





3 


II. 7 


3.2 


2.8 


1-3 


157 


b 


7-915 


8 


907 


6-5 


I 


8 


14.4 


5.4 


3-3 


1.6 


227 


b« 


8.056 


Q 


066 


8.0 


3 


4 


15-7 


7-0 


3-3 


1.6 


290 


6 


6.861 


8 


335 


24.0 


5 


4 


18.6 


9.8 


4.0 


2.2 


278 


V 


8. 154 


TO 


448 


49-5 


20 


5 


19-5 


12. 1 


4-3 


2-4 


244 


8 


7-513 


8 


675 


10. 


4 


6 


14.8 


6.7 


4.8 


1,4 


28.8 


9 


7.762 


8 


390 


5-4 


3 


I 


14.7 


7.2 


4.0 


1.4 


7-5 


10 


7.729 


8 


710 


23.8 


13 


8 


32.6 


18.7 


1-3 


2-4 


71 


11 


7-947 


9 


504 


27.1 


22 


4 


30-5 


21.9 


4-7 


3-2 


149 


12 


7-343 


8 


263 


22.3 


18 


8 


29-5 


20.6 


4.0 


2.3 


205 


13 


7-397 


8 


510 


16.4 


15 


2 


25-7 


15-8 


2.8 


1.6 


221 


14 


9-493 


8 


350 


II. 8 


12 


I 


21.0 


12.3 


2-5 


1-3 


220 


15 


7.5098 


8 


6706 


7-46 






13-74 


5-74 


4-7 


1-4 


24.9 



* Diameters and stroke of cylinder. 



fflRN'S ANALYSIS. 313 

superheated steam reduces Qb, both as compared with the 
total heat appHed and as compared with the value of g^; on 
the other hand, at \ stroke (Experiments 5 and 6), the reverse 
is true. 

It is noticeable that the actual number of calories rejected 
by the walls of the cylinder during the exhaust is almost 
identical in the Experiments 2 and 6, when saturated steam is 
used. The same thing is true of Experiments 9, 10, and 11, 
made on the Corliss engine with a steam-jacket and using sat- 
urated steam. There is more variation of the actual value of 
Q, when superheated steam is used, which may be attributable 
to the varying degree of superheating. 

A steam-jacket reduces the heat rejected by the walls of 
the cylinder during exhaust in a different way. Especially 
when the cut-off is short, as in the experiments given in Table 
XIII, the jacket cannot have much effect on the initial con- 
densation, and almost all of the heat taken by the walls of the 
cylinder before cut-off is furnished by that condensation. 
During expansion a very considerable portion of the moisture 
previously condensed on the walls of the cylinder is evapo- 
rated — much more than would be without a jacket ; and the 
heat thus applied by the jacket does work, though with a re- 
duced efficiency. During the exhaust the jacket furnishes a 
large portion of the heat required to evaporate the moisture on 
the walls of the cylinder at release ; this heat from the jacket 
is thrown away, and would be entirely wasted were it not true 
that the walls of the cylinder are not chilled to the same de- 
gree as when the jacket is not used, and that the initial con- 
densation is thereby reduced. 

The comparison of Experiment 6 with Experiment 11 
may be made to illustrate the preceding statements. In Ex- 
periment 6, 28.3 per cent of all the heat applied is absorbed 
by the walls of the cylinder during the admission : of this less 
than \ is returned during expansion, and f of the heat is 
thrown out as exhaust waste. In the nth Experiment, 15.4 
per cent of the heat applied is absorbed by the walls of the 
cylinder. The heat yielded by the walls of the cylinder during 



314 THERMODYNAMICS OF THE STEAM-ENGINE. 

expansion is f of that absorbed during admission, and \ of the 
amount absorbed is thrown out during exhaust. The excess 
of the heat yielded by the walls of the cylinder during expan- 
sion and exhaust over that absorbed during admission, to- 
gether with the heat lost by radiation, is the measure of heat 
supplied by the jacket. 

To sum up in a few words : It appears that the use of su- 
perheated steam reduces the exhaust waste and consequently 
the initial condensation ; while the use of a steam-jacket, by 
keeping the cylinder hot, reduces the initial condensation and 
increases the re-evaporation, and consequently reduces the ex- 
haust waste. 

Exact conclusions cannot be drawn from the comparative 
economy of the Hirn engine and the Corliss engine. Yet it 
may be stated that these experiments show a gain from the 
use of the steam-jacket of 

8-837— 7.955 
and a gain from the use of superheated steam of 

8.837 

A comparison of Experiments i and 2 shows a gain from 
superheating of 

9:307:r_Z:^^o.i8. 
9-307 

Hallauer, in estimating the gain from the use of superheated 
steam, uses the actual consumption of superheated steam and 
of moist steam, instead of the equivalent dry saturated steam, 
claiming that the superheating was done by waste gases be- 
yond the boiler ; but that is evidence merely that the boiler 
was not economical. 

Inspection of the table shows that in the three tests on the 
Corliss engine the heat yielded by the walls during expansion 
is about I , and the heat rejected during exhaust is about \, of 
the heat absorbed during admission. This, taken with the fact 



HIRN'S ANALYSIS. 315 

already alluded to, shows that the action of the walls was 
nearly the same during each of these phases, while the cut-off 
changed from -jL to ^ of the stroke. 

Before leaving these experiments, attention should be 
called to the fact that in the tests on the Hirn engine the per 
cent of moisture or priming in the exhaust steam has been cal- 
culated from the weight and temperatures of the injection- 
water in the usual calorimetric method. The per cent of 
priming varies with the method of running the engine in some- 
thing the same way as does the per cent of the moisture in the 
cylinder at release ; but it is seldom so much as -|- of the latter 
quantity, and it is never so great as 1 1 per cent. Attention 
will be called to this again in connection with the discussion 
of the question whether the interchange of heat is between 
the steam and the metal of the cylinder, or between the steam 
and moisture remaining permanently in the cylinder. 

In examining the tests on stationary compound engines in 
Table XIV, it is noticeable that while the heat absorbed during 
admission is a considerable fraction of all the heat applied, 
though in most cases less than with a simple engine, the heat 
rejected by the walls during exhaust is in all cases small, and in 
some cases it is insignificant. 

The division of the expansion between the two cylinders of 
a compound engine with the accompanying division of the 
range of temperature reduces the amount of the interchange 
of heat between the steam and the walls of the cylinder, but 
it by no means prevents it. It is postible to make a calcula- 
tion of Qi, which corresponds to the heat restored by the walls 
of the cylinder during expansion in a simple engine ; but here 
that quantity represents a complicated change. During the 
expansion in the small cylinder some of the heat absorbed by 
the walls of that cylinder before cut-off is restored ; during the 
exhaust from the high-pressure to the low-pressure cylinder 
heat is rejected from the walls of the former, a part of which 
is transferred to the walls of the low-pressure cylinder by ini- 
tial condensation therein ; as the expansion goes on in the low- 
pressure cylinder, before and after cut-off of that cylinder, the 



3i6 



THERMODYNAMICS OF THE STEAM-ENGINE. 



lowering pressure is accompanied by re-evaporation of water 
from its sides, and heat is yielded therefrom. Consequently 
the calculation corresponding to the finding of Qj, develops 
positive and negative quantities whose sum is not a measure of 
the action that actually takes place. The only way of properly 
investigating this action is that suggested by the application of 
Hirn's analysis to compound engines on page 222, and the data 
for it are not given for these tests by Hallauer. 

The data of the experiments on marine engines were fur- 
nished by M, Widman ; the results stated in Table XV were 
calculated by Hallauer. It was not possible to measure the 
amount of coohng water used per stroke, consequently the 
check given by the condenser on the value of Q, could not be 
obtained. On the other hand, the use of the surface condenser 
gave a very exact method of measuring the consumption of 
steam. 

The engine of the Duquesne has six cylinders, arranged to 
form three Woolf engines, with the small cylinder of each 
above the large cylinder. From the positions of the cylinders 
the intermediate receiver had a considerable volume. Two 
series of experiments were made: i, 2, and 3 show the effects 
of throttling the steam, and 1,4, 5, 6, and 7 show the effect of 
shortening the cut-off. Hallauer has modified the results in a 
manner already alluded to and has used the second results in 
his comparisons. 

Experiments i and 3, Table XV, and 15 and 16, Table 
XIV, are compared in^the following table: 



Indicated horse-power 

Reduction of pressure by throt- 
tling 

Percentage of water: 

Small cylinder cut-off 

Small cylinder release 

Large cylinder release 

Consumption in kilos: 

Total horse-power 

Indicated horse-power 

Heat rejected to condenser. . 



Duquesne. 


Diff. 


1410 


8490 




.... 


20 1 GO 




4.0 

2.7 

II. 


2.4 
2.2 

9-3 


1.6 

0-5 
1-7 


8.832 
11.242 
3.7 


8.416 

9-405 
1.9 


0.416 

1.837 
1.8 



Woolf. 



178 

9.10 

10.8 
10.4 
10.6 



367 



3010 



9.4 
8.9 
9.6 



7.316 7.042 
9.145 8.354 
6.4 4.9 



Diff. 



1.4 

1.5 

0.7 

0.274 
0.791 
1-5 



BIRN'S ANALYSIS, 317 

Hallauer considers the parallelism exhibited by this table 
to be a verification of the tests on the marine engine, in de- 
fault of the check afforded by measuring the cooling water. 

The interchange of heat between the walls of the cylinder 
and the steam is roughly indicated by the per cent of water in 
the cylinder at the several points indicated. In the first four 
experiments, where the power is varied by throttling, these 
percentages and the value of Q,, rejected to the condenser, 
vary in an irregular manner and to a small amount only. On 
the other hand, the increase of these several quantities is 
marked and regular when the power is regulated by shorten- 
ing the cut-off. It is also apparent that the consumption is 
reduced by increased expansion as far as to eight expansions, 
though the ratio of the volumes of the cylinders is ill adapted 
to large expansion, and that it increases rapidly for more than 
eight expansions. 

The performance of the engine of the Diiquesne with a 
variable cut-off may be compared with the stationary Woolf 
engine. Table XIV, Experiments 17 and 18. For example, the 
marine engine, when exerting 3900 horse-power, with 8 expan- 
sions, has 9.8 per cent for the value of Q^, while the stationary 
engine, exerting 220 horsepower, with 13 expansions, has Q^ — 
10.2 per cent. Again, compare the consumption per total 
horse-power of the marine engine, when exerting 1665 horse- 
power with 20 expansions, with that of the stationary engine 
exerting 150 horse-power with 26 expansions. The latter has 
the advantage by 

8. 1 54 -6.83 1 



8.154 



= 0.162. 



Of course some of this may be attributed to the greater 
degree of expansion of the latter, but the real explanation is 
to be sought in the methods of obtaining the expansion. The 
ratio of the cylinders for the stationary engine is i : 5|-, and the 
expansions in the small cylinder are 5. On the other hand, 
the ratio of cylinders for the marine engine is 1:2, and the 
expansions in the small cylinder are 10. This large degree of 



3l8 THERMODYNAMICS OF THE STEAM-ENGINE. 

expansion in the small cylinder of the marine engine causes an 
initial condensation of 49 per cent, while that of the stationary 
engine is 39 per cent. 

The test 19, in Table XIV, is remarkable for the small con- 
sumption of steam per horse-power per hour, though the total 
horse-power was only 78.5. This engine was a portable com- 
pound condensing engine, having a distribution slide-valve and 
an independent cut-off valve for the small cylinder, and a plain 
slide-valve for the large cylinder. In 1878 a medal was offered 
by the Societe Industrielle de Mulhouse for the first compound 
engine constructed in Upper Alsace, that should give one brake 
horse-power (cheval a vapeur) for less than 9 kilograms of steam. 
This engine was offered for trial, and was tested by a committee 
and awarded the medal. 

Isherwood ^ gives, on page 319, the table of data and results 
of tests transferred to the English system of units. 

Mair's Steam-engine Tests. — In Table XVII are given 
the data and results of a number of tests on large engines of 
various types, reported by Mr. George Mair,f together with a 
very complete analysis according to Hirn's method. 

In all of these tests the power was measured by indicators 
that were tested after every trial, and diagrams were taken at 
intervals of 15 or 20 minutes, which were measured by a planim- 
eter. The mechanical equivalent of heat was assumed to be 
772 foot-pounds for facility in use of tables of the properties 
of steam, though reference is made to Joule's later determina- 
tions. 

The steam consumption was determined by measuring the 
feed-water supplied to the boiler. The steam condensed in the 
steam-jackets was collected and weighed separately. The air- 
pump discharge was allowed to flow through an orifice under a 
measured head ; the coefificient of discharge for the orifice was 
determined by direct experiments. The per cent of priming 
in the steam was determined by calorimetric tests. In the test 

* Jour^aal Franklin Inst., vol. cxx., Oct. 1885. 

f Proc. of the Inst, of Civ. Engs., vol. Ixx. page 313, and vol. Ixxix. page 
323. 



HIRN'S ANALYSIS. 



319 



TABLE XVI. 
Experiments on a Condensing Compound Engine. 



Total Quantities. 

Duration of the experiments, hours 

Revolutions 

Pounds of feed- water pumped into the boiler 
Pounds of condensing water 

Engine. 
Steam-pressnre in boiler in ponnds per 

square inch above the atmosphere 

Pressure in the condenser in pounds per 

square inch above zero 

Num ber of revolutions per minute 

Position of the throttle-valve 

Cut-off, small cylinder 

Release, small cylinder 

Compression, small cylinder 

Cut-off, large cylinder 

Release, large cylinder 

Compression, large cylinder 

Number of times the steam was expanded. . 
Atmospheric pressure in pounds per sq. inch 

Temperatures. 

Temperature in degrees Fahrenheit of the 
condensing water when admitted to the 
condenser 

Temperature in degrees Fahrenheit of the 
condensing water and water of steam con- 
densation when taken from condenser 

Absolute Steam-pressures in Small 
Cylinder per Indicator. 

At commencement of stroke 

At point of cut-ofE 

End of stroke 

Mean back pressure 

At compression 

Indicated pressure 

Absolute Steam-pressures in Large 
Cylinder per Indicator. 

At commencement of stroke 

Point of cut-off 

End of stroke 

Mean back pressure 

At compression . . 

Indicated pressure 

HoRSE-POWER. 

Indicated horse-power developed in the 
small cylinder 

Indicated horse-power developed in the 
large cylinder 

Aggrei^ate indicated horse-power devel- 
oped by the engine 

Horse-power developed by the engine at 
the friction-brake 

Economic Results. 

Pounds of feed-water per hour per indi 
cated horse-power 

Pounds of feed-water per hour per brake 
horse-power 

Fahrenheit units of heat per hour per indi- 
cated horse-power 

Fahrenheit units of heat per hour per brake 
horse-power 



July 7, 1879. 
Morning. 



16014. 

3951. 

73821. 



91.78 



Wide open. 
0.42 
0.98 
0.925 

0-45 
0.91 

0-75 
6.26 
14.22 



95-7 



100.8 

89.3 
44.1 
45-3 
41.6 
30.2 



430 

27-5 
12.3 
3-8 
2.4 



24.8 
52.4 

77.2 
67.7 

17.7 

19-5 
19110. 
21785. 



Wide open, 
0.42 
0.98 
0.925 

0.45 
0.91 
0.7s 
6.26 
14.22 



July 7, 1879. 
Afternoon. 



4.00139 
21253. 
5379- 
98621. 



91.52 



102.5 
91.0 
44.9 
46.2 

42.4 
30.8 



43-2 
27.7 
12.5 
3-8 
2.4 
22.3 



25.2 
52.5 
77.6 

67-5 

17.3 

19.9 
19351- 
21960. 



3.00222 
16211. 
3248. 
74039- 



91.69 

1. 81 
90. 

Wide open, 
0.25 
0.98 
o 925 

0-45 
0.91 
0.75 
9.64 
14.22 



July 8, i879.ijuly 8, 1879, 
Morning. Afternoon. 



48.0 
86.9 



99.8 
88.3 
33-4 
35-3 
34-8 
27.8 



34-5 
21.16 
9.6 
3-8 
2.4 
17.0 



23.1 
40.7 
63.9 

55-7 

16.9 

19.4 
19108. 
21906. 



3.24139 
17253- 
4265. 
78894. 



92.16 

1. 91 

88.7 

Wide open. 

0.42 

0.98 

0.92s 

0.45 

0.91 

0.75 

6.26 

14.22 



48.0 
96.7 



103.0 
91-5 
45-2 
46.4 
42.6 
30-7 



43-2 
27.7 
12.6 
3-8 
2.4 
22.3 



25.1 

52.7 
77.8 
67.5 

16.9 

19-S 
18924. 
21804. 



320 THERMODYNAMICS OF THE STEAM-ENGINE. 

C the condensation in steam-pipe was drained into buckets and 
weighed ; in the test B the condensation in the steam-pipe 
flowed to the engine, and an allowance was made depending on 
the condensation caught during the test C. In all the other 
tests the steam-pipes drained toward the boilers. 

The test A was. made on a single cylinder rotative pump- 
ing-engine, having a diameter of 45 inches and a stroke of 5 
feet 6 inches. The sides and ends of the cyHnder were jack- 
eted with boiler steam. The steam was distributed by sepa- 
rate slide-valves near the ends of the cylinder, with expansion- 
plates adjustable by hand, on the backs of the main valves. A 
surface condenser was used. Three tests were made on this 
engine, each of which gave the same result ; one test only is 
therefore given in the table. The engine had been at work 
nine months when tested ; it was carefully examined, and the 
piston and valves were tight and in good order. 

The tests B and C were made on a Woolf beam rotative 
engine, working a deep-well pump direct from the beam, which 
had been working six months when tested. The cylinders 
were 22 inches in diameter by 3 feet 7 inches stroke, and 
34 inches diameter by 5 feet 6 inches stroke, and were 
jacketed with boiler steam on the sides and ends. The steam 
was distributed by a long slide with equilibrium passages in it, 
and expansion-plates on the back, worked by eccentrics ; there 
was a jet condenser, and the air-pump discharge was measured. 
Two tests were made — one with and one without steam in the 
jackets. 

The tests D, E, and F were made on a Woolf beam-engine 
driving a flour-mill. The cylinders were 2^\ inches in diame- 
ter by 3 feet 5 inches stroke, and 38 inches diameter by 5 feet 
6 inches stroke, and were steam-jacketed on the sides only. 
The steam was distributed to the high-pressure cylinder by a 
slide-valve with cut-off plates on the back, and to the low-pres- 
sure cylinder by a piston-valve, all being worked by eccentrics. 
The steam was condensed in a surface condenser. Three tests 
were made — two with and one without steam in the jackets. 

The tests G and H were made on an unjacketed horizontal 



HIRN'S ANALYSIS. 



321 



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THERMODYNAMICS OF THE STEAM-ENGINE. 



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HIRNS ANALYSIS. 



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324 



THERMODYNAMICS OF THE STEAM-ENGINE. 



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HIRN'S ANALYSIS. 325 

Woolf engine, of a type very commonly used in factories in 
Lancashire. The cylinders were 15! and 28|- inches in diame- 
ter by 4 feet 3 inches stroke. The piston speed was about 680 
feet per minute and the load was light, so that the steam was 
mu*ch v/ire-drawn. Three trials were made, during which the 
boiler-feed and air-pump discharge were measured ; the first test 
was not reported, as the engine was stopped during the test. 

The test I was made on a compound beam receiver engine 
with the cranks at right angles, working pumps directly from 
the beams. The cylinders were 21 and 36 inches in diameter, 
and the stroke was 5 feet 6 inches. Both cylinders, with the 
exception of the high-pressure cylinder and the receiver-covers, 
were jacketed with boiler steam. The steam was distributed 
by slides, one at each end of each of the cylinders, with cut-ofT 
plates adjustable by hand. A jet condenser was used, and the 
air-pump discharge was measured. Two tests were made, giv- 
ing the same result, so that only one was reported. 

The test K was made on a Cornish engine working a single- 
acting piston pump direct from the beam, and having the 
usual Cornish, double-beat, steam, equilibrium, and exhaust- 
valves, a single-acting air-pump, and a jet condenser ; the cyl- 
inder was 68^ inches in diameter by 8 feet stroke, and was 
jacketed on the sides with boiler steam. The pump delivered 
its water on the up or steam stroke, so that the preponderance 
of weight on the pump-pole was only enough to overcome 
the suction lift. The valves and piston were inspected to as- 
sure their tightness before the test. The engine was doing 
the highest duty at the West Middlesex Waterworks, and was 
taken as one of the best engines of its type now working. 
This type of engine was developed in Cornwall, where it was 
used to pump water from deep mines by a pump-rod hung 
directly from one end of the beam while the piston was hung 
from the other end of the beam. It had no fly-wheel, but the 
pump-rod, beam, and counter-weights made in the aggregate 
a large reciprocating mass, that absorbed work during the first 
part of the stroke when the steam-pressure in the cylinder was 
high, and restored that work and assisted the steam to com- 



326 THERMODYNAMICS OF THE STEAM-ENGINE. 

plete the stroke after it has lost pressure through expansion^ 
during the latter part of the stroke. Such a reciprocating 
mass is essential to the proper action of the engine with a good 
degree of expansion. The pumps of the original engines were 
worked by the weight of the rods during the return or equi- 
librium stroke, at which time there was free communication 
between the two ends of the cylinder. The lower end of the 
cylinder was open to the condenser during the steam-stroke. 

The tests L and M were made on a single-cylinder beam 
rotative pumping-engine, having a diameter of 32 inches and a 
stroke of 5 feet 6 inches. The cylinder sides and base were 
jacketed with boiler steam. Steam was distributed by slide- 
valves at the top and bottom of the cylinder, with cut-off 
plates, adjustable by hand, on the backs of the main valves. 
There was a jet condenser, but the air-pump discharge could 
not be measured. 

The tests N and O were made on a single-cylinder beam 
rotative engine, similar to the one just described, and taking- 
steam from the same boilers. The cylinder was 27 inches in 
diameter, by 6 feet stroke. 

The test P was made on a Bull engine with a cylinder 68 
inches in diameter by 10 feet stroke, driving direct a 45-inch 
plunger-pump, and forcing water to a height of 40 to 55 feet. 
The valves and gear were of the usual Cornish pattern, and the 
sides and base of the cylinder were steam-jacketed. This type 
of engine differs from the Cornish engine in not having a beam,, 
and though the pump-rod is loaded there is seldom sufficient 
reciprocating mass to allow of much expansion. In the case of 
the engine tested only if expansions could be obtained. For 
convenience, the steam-stroke is detailed under the heading of 
the high-pressure cylinder, and the exhaust-stroke under the 
heading of the low-pressure cylinder. 

The tests Q and R were made on a Woolf beam rotative 
engine, working a double-acting pump. The cylinders were 29 
inches diameter by 5 feet 5 inches stroke, and 47^ inches 
diameter by 8 feet stroke, and jacketed with steam on the sides 
and ends. Steam was distributed by slide-valves with adjust- 



HIRN'S ANALYSIS. 327 

able cut-off plates to the high-pressure cylinder ; the exhaust- 
valves are double-beat valves worked by cams. 

The interchanges of heat between the steam and the walls 
of the cylinder in these tests are calculated by a process that 
is equivalent to that indicated by equations (256) to (259). To 
make the matter clear, and to explain some of the headings of 
Table XVII, the entire calculations for the test I are given 
here. 

The engine was compound, steam-jacketed, with an interme- 
diate receiver, and ran at an average speed of 23.98 revolutions 
per minute and expanded the steam 13.61 times. The absolute 
boiler-pressure was 76 pounds, and the indicated horse-power 
127.4. The air-pump discharge was 25.558 pounds per stroke, 
the initial and final temperatures being 50°.o and 73°.4 F. 

The weights of water and steam per stroke were : 

Pounds. 

Boiler delivery, 0.69693 

Steam through cylinders, .... Mx = 0.58338 

Priming, M{i — x) = 0.02430 

Condensation in jackets, My =: 0.08925 

Injection-water, G =: 24.95 

The heat brought into the high-pressure cylinder of the en- 
gine per stroke is 

Q = MxX + M{i —;i;)^ = 0.58338 X 1 1 76 + 0.0243 X 278.58 

^ 686.06 + 6.76 = 692.82 B. T. U., 

in which X is the total heat and g the heat of the liquid corre- 
sponding to the pressure of the entering steam. Let r be the 
heat of vaporization at the same pressure, then the heat sup- 
plied by the steam-jackets is 

Qj+ Q; = 0.08925 X 897.45 = 80.09 B. T. u. 

The total amount of heat delivered to the engine per stroke 
is 

+e,+ G/ = 772.91 B.T.U. 



328 THERMODYNAMICS OF THE STEAM-ENGINE. 

The heat retained by the condensed steam at the tempera- 
ture t^ of the air-pump discharge is 

M{t, — 32) = 0.60768(73.4 — 32) = 25.16 B. T. U. 

So that the heat used by the engine per stroke was 

772.91 — 25.16 = 7/1^7.7^ B. T. U. 

The thermal units per horse-power per minute, calculated 
from 32° F., was 

772.91 X 2 X revolutions 772.91 X 2 X 23.98 ^ ^ ^^ 
ILR = 1^74 " '^'•'' ^'^' ^' 

The number of pounds of dry steam consumed per horse- 
power per hour was 

772.91 X 2 X revolutions X 60 772.91 X 2 X 2398 X 60. 
H. P. X A. ~~ 127.4 X 1 176 

= 14.84 pounds. 

The actual number of pounds of moist steam used per horse- 
power per hour was 

0.69693 X 2 X 23.98 X 60 , 

— ^-^ ^-^ = 15.7 pounds. 

127.4 "^ ^ ^ 

Both of these results show exceptionally high economy of 
the use of steam at an absolute pressure of 76 pounds. 

The density of the steam in the cylinder at different points 
of the stroke was calculated by aid of an adaptation of Zeuner's* 
formula 

y = 0.606 1/°^393^ 

which for English units may be written 

log> = 0.9393 log/ - 2.51853. 

* Mechanische Warmetheorie, page 294. 



HIRN'S ANALYSIS. 329 

At cut-off in the high-pressure cyHnder, for example, the 
absolute pressure was p^ = 64 pounds ; and the density, or 
weight in pounds of one cubic foot, of dry steam at this pres- 
sure, is by the formula 7/^ = 0.1506 pounds. The volume of 
steam at cut-off, allowing for clearance, was 2.9161 cubic feet; 
hence the weight of dry steam at cut-off was 

2.9161 X 0.1506 = 0.4392 of a pound. 

By a similar calculation the weight of dry steam caught at 
the beginning of compression was found to be 0.05913 of a 
pound. This added to the weight of moist steam per stroke 
gives for the weight of the mixture in the cylinder 

0.60768 + 0.05913 = 0.66681 of a pound. 

Consequently the per cent of water in cylinder at cut-off 
was 

0.66681 — 0.4392 

100 X -^^z^ ^- = 34.1 per cent. 

0.66681 "^^ ^ 

The heat equivalents of the intrinsic energy of the mix- 
ture in the cylinder at cut-off, release, compression, and admis- 
sion are given by the equations 

I, = {M-^rM,){x,p,Jrqy. .... (294) 

I^ = {M+M,){x,p, + q,)', .... (295) 

/3 = J/,(;^3P3 + ^3); (296) 

I, = Mlx^p,^q,)', (297) 

in which M is the weight of moist steam through the cyhnders 
per stroke, and M^ is the weight of steam caught at compres- 
sion, on the assumption that the steam is then dry and satu- 
rated ; and x is the part of one pound of the mixture that is 
steam ; and p and q are the heat equivalent of intrinsic energy 
and the heat of the liquid, at the several points mentioned. 



330 THERMODYNAMICS OF THE STEAM-ENGINE. 

For the high-pressure cylinder Mr. Mair writes 

Qa^Q^-h-h-AW^', (298) 

a = /.-/. + ^^.; (299) 

a = Ga+a+Gy-a-a; . . . (300) 

a = /3-/o + ^^.; (301) 

The equation for Q, is obtained by aid of the equation 

a+G.+a-G^+a+a,. . . . (302) 

which asserts that the heat absorbed by the cylinder walls dur- 
ing admission and compression, together with the heat given 
up by the steam in the high-pressure jacket, is equal to the 
heat yielded during expansion and exhaust, plus the heat lost 
by radiation. For the low-pressure cylinder he gives the equa- 
tion 

Q. + QI + <2/ = e/ + fi/ + G/ , . . . (303) 

which asserts that the low-pressure cylinder walls receive the 
heat Qc rejected from the high-pressure cylinder during ex- 
haust, the heat absorbed by the wall during compression, and 
the heat yielded by the steam condensed in the low-pressure 
jackets, and that this heat is equal to that yielded by the walls 
during expansion, during exhaust, and by external radiation. 
The quantity Q^ is that complex quantity described on page 
222, and it is assumed that it applies to the whole stroke of 
the low-pressure piston, both before and after cut-off. For the 
low-pressure cylinder he gives 

!2/ = //-(/,-/3 + // + ^fr,) + ^fF/; . (304) 

e/ = a+G/ + G/-a'-G/; (305) 

Qi^i:-i:+Aw^ (306) 

Equation (306) is of the same form as equation (250), and 
equation (305) is obtained from equation (261). To find Q^ it 
is assumed that the difference between the heat equivalents of 
the intrinsic energy at release and compression in the high-pres- 
sure cylinder is thrown into the low-pressure cylinder, together 



HIRN'S ANALYSIS. 33 1 

with the heat equivalent of the absolute work during exhaust 
from that cylinder, and that to this sum is to be added the 
heat equivalent of the intrinsic energy of the steam at the 
end of compression in the low-pressure cylinder. 
For the test I we have 

a == 692.82 + 33.36 - 540.80 - 37.49 = 147.89 B. T. U. ; 

Q, = 583.70 - 540.80 + 54.61 = 97.5 1 B. T. U. ; 

Qa = 63.54 - 33.36 + 7.14 r= 37.32 B. T. U. ; 

a = 147-89 + 37-32 + 32.43 -97.5 1 -7.00= 113.13B.T.U.; 

e; = 546.82 - (583.70 - 63.54 + 17.89 + 31.47) + 72.69 ; 

= 49.99 B.T.U.; 
G/ = 10.60 - 17.89 + 0.60 = - 6.6g B. T. U. ; 
Q/ = 1 13.13 - 6.69 + 47.66 - 49.99 - 15.72 = 88.39 B. T. U. 

The engine on which test I was made had a jacketed re- 
ceiver, and in this calculation as well as in Table XVII the 
condensation in the receiver jacket is added to that in the low- 
pressure jacket, and the radiation from the receiver is added to 
that from the low-pressure cylinder. 

In the table these several quantities of heat are stated in 
percentages of the heat used by the engine per stroke, that is, of 

Q + Qj+Q/-Mg„ 

to facilitate the comparison of tests made on different engines. 
Discussion of Results. — The effect of a steam-jacket on 
a single-cylinder engine may be seen by comparing the tests 
L and M. With a loss of only one pound boiler-pressure, it 
was found necessary to reduce the expansions from 4.33 to 3.84, 
in order to obtain the same power without the jacket in M as 
with the jacket in L. Comparing the B.T. U. per horse-power 
per minute, the gain from the use of the steam-jacket, and the 
greater expansion that could then be used, is 

515.9 — 430.0 
100 X = 16 per cent. 



332 THERMODYNAMICS OF THE STEAM-ENGINE. 

Comparing the interchanges of heat between the walls of 
the cylinder, it appears that the use of the steam-jacket reduces 
the heat Q, rejected during exhaust, and consequently the ini- 
tial condensation, as shown by g^, while the external radiation 
is a little larger with a jacket than without. 

Comparing the tests B and C made with and without steam- 
jackets on a compound Woolf engine, there appears to be a 
gain of 

519-5 — 338.8 
100 X — ^ = 34 per cent • 

but this difference is largely due to the fact that in the test C 
the steam-pipe was well drained, and in the test B it was not. 
Comparing the tests E and F, the gain from the use of the 
steam-jackets and of the larger expansion then possible is 

378.1— 341.8 
100 X — ^- — loj per cent, 

which would probably be increased were the ends of the cylin- 
ders jacketed as well as the sides. In this case, with the larger 
degree of expansion accompanying the use of the jackets, it 
appears that the initial condensation in the high-pressure cylin- 
der is not greatly affected, and Q^ is nearly the same in both 
tests ; but the heat restored during the expansion in the high- 
pressure cylinder Q^, and in the low-pressure cylinder Qy, are 
both increased, so that g/, the exhaust waste, is reduced from 
22.4 per cent to 9.6 per cent. 

The steam consumption in the test I is remarkably low, 
showing an excellent adaptation of the engine to its work. It 
is interesting to compare the interchanges of heat in this test 
with those in the tests T and U, which give nearly as good an 
economy, and with other tests giving a poorer economy. It is 
noteworthy that the exhaust waste g/ for the tests of com- 
pound engines given in Table XVII cannot be regarded as a 
measure of the economy of the engine, neither can that engine 
be said to be working under the best conditions which shows 



HIRN'S ANALYSIS. 333 

in general the snnallest interchanges of heat between the steam 
and the walls of the cylinder. The best result appears rather 
to be attained by a judicious or fortunate compromise of the 
gain from expansion and the loss from condensation and evap- 
oration, and of the amelioration of the latter by the use of 
steam-jackets in which heat is usefully applied for that purpose, 
though with a loss of thermodynamic efficiency. 

Institute of Technology Tests. — The data and results of 
tests made on a Harris-CorHss engine in the laboratory of the 
Massachusetts Institute of Technology are given in Table 
XVIII. This table is given in part to afford examples to which 
the equations for Hirn's Analysis on page 192 may be applied 
by the student. 

The engine is an automatic cut-off unjacketed engine using 
saturated steam. The stroke is 24 inches and the diameter is 
8 inches. During the tests the governor was disconnected, the 
cut-off was fixed, and the speed was regulated by another 
engine coupled with this engine. Both the condensed steam 
and the cooling water from a surface condenser were weighed 
in tanks. 

Water in the Cylinder. — As a conclusion of his analysis 
applied to his own and to Hallauer's engine tests, Hirn * con- 
cludes that all the theories of the steam-engine proposed by 
writers on thermodynamics, based on the hypothesis that the 
interaction between the steam and the walls of the cylinder 
is inconsiderable, are liable to be in error to the extent of 
50 per cent, and are consequently entirely useless and mis- 
leading. In reviewing these experiments and the conclu- 
sions from them, Zeunerf developed the equations (256) to 
(259) substantially as given on page 189; and, in addition to 
pointing out that the possible effect of eddies and mechanical 
motion of the steam in general had been neglected, and that 
the method of calculation given on page 307 is inaccurate, he 
called attention to the fact that a thin layer of water adhering 

* Th6orie m6canique de la Chaleur, vol. ii. p. 68. 
f Civil-ingenieur, xxvii. 



334 



THERMODYNAMICS OF THE STEAM-ENGINE. 



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HIRN'S ANALYSIS. 335 

to the walls of the cylinder and participating in the changes of 
temperature, would account for the larger part of the disturb- 
ances attributed to the action of the metallic walls of the cylin- 
der. It consequently becomes of great importance to deter- 
mine J/q, the weight of the mingled water and steam caught in 
the cylinder at compression. The effect of the mechanical 
motion of the steam in the cylinder during expansion cannot 
be considerable, and the errors of the method of calculation 
employed are insignificant. 

To investigate the probable value of M^^ Hallauer* recalcu- 
lated a number of the tests given in Tables XII and XIII 
under various assumptions. For the test of Sept. 8, 1875, he 
finds that the value of Q,^ the exhaust waste, is 37.02 calories, as 
given in Table XIII, when calculated on the assumptions that 
the steam caught in the cylinder at compression and the work of 
compression can both be neglected. Assuming that the steam 
caught at compression is dry and saturated, and allowing for 
the work of compression, he finds that Q^ == 38.52 calories. 
The weight of steam caught at compression he finds to be 
0.00432 kilogram under this supposition. He then assumes 
that just enough water is present in the cylinder at compres- 
sion to give the same intrinsic energy for the mixture at the 
beginning and end of compression, calculated from the known 
volumes and pressures at those points. The weight of the steam 
and water in the cylinder during compression is 0.05082 kilo- 
gram on this supposition, and the exhaust waste is Q^ = 38.17 
calories. The differences of the three values of Q^ thus deter- 
mined are less than the probable error of the experiment. It 
should be noted that the weight of steam exhausted from the 
engine per stroke was 0.2634 kilogram, and that the moisture 
in this steam was 10.63 per cent, as determined from the initial 
and final temperatures of the injection-water. 

Finally, Hallauer finds that if it be admitted that the weight 
of water and steam caught in the cylinder at compression is 
equal to that exhausted per stroke, — an assumption which 

* Bulletin de la Soc. Ind. de Mulhouse, vol. Iv. 1881. 



336 THERMODYNAMICS OF THE STEAM-ENGINE. 

Zeuner claims to be reasonable, and which would require only 
a thin layer of water adhering to the cylinder walls, — then he 
finds that the walls of the cylinder must have yielded 12.22 
calories during compression ; an amount which may be consid- 
ered absurd. At the same time he finds that this particular 
assumption makes Q, — 42.66 calories, or that it involves a 
larger exhaust waste. 

If it be assumed that the interchange of heat between the 
steam and the walls of the cyHnder during compression is in- 
considerable in the test of Nov. 28, 1873, Hirn * finds that the 
equations given by Zeuner give for the interchange of heat 
between the steam and the walls of the cylinder 

Q^ = 52.61 calories — GS.^gG^ ; 
Qi, = 21.07 calories — 43.296^^ ; 
Q, = 31.5 calories — 25.3(^0 ; 

the several values of Q being successively for admission, ex- 
pansion, and exhaust, and G^ being the weight of water and 
steam caught in the cylinder at compression, which is assumed 
to be unknown so that there are four unknown quantities with 
three equations. 

If it be assumed that the steam is dry and saturated at 
compression, then for this test G^ = 0.00112 kilogram, and 

Qa = 52.53 calories; 
Qi, = 21.02 calories; 
Q, = 31.47 calories. 

On the other hand, if it may be assumed that any one of 
the three quantities Q^, Qg,, or Q^ is inconsiderable, and can be 
neglected, then G^ may be calculated directly. First suppose 
that Qi, is zero, or that there is no interchange of heat during 
expansion ; then 

Go = 0.487 kilogram ; 

Qa= 19.21 calories; 

Q, = 19.18 calories. 

* Bulletin de la Soc. Ind. de Mulhouse, vol. lii,, 1882. 



HIRN'S ANALYSIS. 33/ 

Now the weight of vapor exhausted per stroke is 0.3732 kilo- 
gram, so that the assumption requires that the weight of water 
in the clearance shall exceed the weight of steam exhausted. 
But while this condition is supposable, it is impossible that the 
walls of the cylinder should receive heat from the steam during 
exhaust, as is indicated by the positive sign. 

If it be assumed that there is no exhaust waste, that is, that 
Q, r= o, then 

G^ = 1.245 kilograms; 

Q^=i — 32.78 calories ; 

0^, = + 32.78 calories ; 

which would require that the walls during admission should 
yield heat to the entering steam, and that they should absorb 
heat during expansion. 

The conclusion is inevitable, that there is an energetic inter- 
change of heat between the steam and the walls of the cylin- 
der. It also seems probable that there cannot be great error 
in assuming that the steam is dry and saturated at com- 
pression. 



CHAPTER XVIII. 

VARIOUS STEAM-ENGINE TESTS. 

Tests on Donkin Engines. — A large number of efficiency 
tests were made by Mr. Bryan Donkin, Jr., and Mr. Salter on an 
engine built for the purpose by Messrs. B. Donkin & Co.,* in 
which the methods of making the tests and calculations were 
similar to that outlined on page 242. 

The engine was a two-cylinder tandem compound engine ; 
each cylinder was provided with a steam-jacket, which could be 
supplied with steam in various ways, and the water condensed 
from each jacket could be drawn off and weighed separately. 
Each cylinder had the steam distributed by a plain slide-valve, 
and the small cylinder had a cut-off valve on the back of the 
main valve. 

The heat brought into the cyHnder of an engine may be 
divided into three parts : one part is changed into work, a sec- 
ond part is lost by radiation, and a third part is carried away 
by the condensing water. In these experiments the part 
changed into work was determined by taking indicator-dia- 
grams at regular intervals ; the power of the engine was also 
measured by a friction brake. The heat carried away by the 
condensing water was determined by taking the temperature 
of the injection-water before it was delivered to the jet-conden- 
ser, and the temperature of the mingled condensing water and 
condensed steam discharged by the air-pump, and by gauging 
the latter on a weir i^ inches wide. Allowance was made for 
the water condensed in the jackets when they were in use. The 
heat lost by radiation was not determined, but was assumed to 

* Engineering, vol. xxi. p. 203; vol. xl. pp. 317 and 342; vol. xlii. pp. 487 
and 577. 

338 



VARIOUS STEAM-ENGINE TESTS. 339 

be small in amount, and nearly if not quite constant. The 
number of thermal units carried away by the condensing water 
per indicated horse-power per minute was considered to be the 
measure of the economy of the engine ; that is, it was considered 
that the most economical method of running the engine was 
that one in which this quantity was smallest. 
The dimensions of the engine were : 

Diameter, small cyHnder, 6 in. minus ^is" i^- 

large '' lO '^ '' -gV '' 

Stroke, i foot. 

Piston displacement : small cylinder, . . 336.4 cu. in. 

large '' . . 939.1 " '' 

r^y n T J Cubic Per cent of small 

Clearance, small cylmder : inches. piston displacement. 

crank end : clearance (f in.), 17.5 5.2 

passage, 24.3 7.22 

back end : clearance (^^ in.), 17.5 5.2 

passage, 24.3 7.22 

Clearance, large cylinder: SjhS. pSondisV'iicJment. 

crank end : clearance, (|- in.), 6y.y 7.2 

passage, 26.9 2.86 

back end : clearance, 64.2 6.84 

passage, (f in.), 27.8 2.96 

Small-cylinder exhaust passage and ] ,0^ ^ 

large-cylinder steam-chest, ) 

The ratio of expansion is calculated as follows : The cubic 
contents of the low-pressure cylinder -\- the cover end-clearance 
and passage -\- high-pressure exhaust passage and low-pressure 
steam-chest -f- the high-pressure cylinder -|- the front clearance 
and passage = 1589.8 cubic inches. The cubic contents of the 
high-pressure front clearance and passage =41.8 cubic inches. 

Total cubic content = 1589.8 

•pr-T' : — rT~7 :: 1 — 7? = ratio of expansion. 

Cubic content beiore steam is cut on ^ 

The experiments to determine the friction of the engine 
were made with the steam at 40 lbs. pressure in the boiler. 



340 THERMODYNAMICS OF THE STEAM-ENGINE. 

Steam was passed through the jacket of the low-pressure cylin- 
der before it reached the engine, but there was no steam in the 
jacket of the high-pressure cylinder. The stop-valve was nearly 
closed, and the governor was connected to the throttle-valve ; 
the cut-off was at about one eighth of the stroke. The brake 
strap was lifted off the fly-wheel, and when the revolutions 
were steady three sets of indicator-diagrams were taken. Sev- 
eral experiments were made, and a fair average of the whole, 
with the speed at 96 revolutions, gave the friction as 1.37 
horse-power. 

Table XIX gives the data and results of tests made (i) 
with no steam in either jacket, but with air in both ; (2) with 



600 








f^:No.-Jacket) 




650 

62 


^JU^ — 




500 






69 ' '•^^ 
400 ®34 ^^ 


X^^, Small Cyluider:Jacket' , --•S»P^'^ 


300 \ 


8 9 10 11 12 

1 1 1 1 1 


13 



Fig. 62. 

Steam passed through the jacket of the high-pressure cylinder 
to the steam-chest of that cylinder, and with air in the low- 
pressure jacket; (3) with steam in the low-pressure jacket only; 
(4) with steam passed through the low-pressure jacket, thence 
through the high-pressure jacket, and thence to the high-pres- 
sure steam-chest ; (5) with the steam throttled and passed 
through the low-pressure jacket and thence to the high-pressure 
steam-chest. The results of the first four series of tests are 
also represented by Fig. 62, in which curves are drawn with 



VARIOUS STEAM-ENGINE TESTS. 



341 



TABLE XIX. 
Tests on Donkin Engine. 





, 


3 


V. 








Horse- 


Tempera- 
ture of con- 


<u 




c 


a 




Conditions 


C 

a 

a 


a 


a 
.2 
c 




"0 

tn 

V 
Xi 



power. 


densing 
water. 


^1 
'oS 


^1 

"0 (U 


















■c^ 




of Test. 


en 
C 





2 


11 


c . 


T3 








■5 & 

.fa 


.0 5i 






3 



0:3 


.2 


^•- 


it 

3 V 




6 


2 



a 


in'*" 


1.1 


e^ 








> 


3 « 


rt 


Ss 


^^ 


•0 

a 


rt 


1 


§e 


§a 


1^ 


c rt 






Oi 


U 


Di 


Q 


> 


eq 


u 


^ 


cu 


H 


S 


56 
63 


No jackets on. 
Boilure-pres- 
sure, 43 pds. 


96.61 


^ 


8.38 
7.54 


30 
30 


'-^5-9 
26.2 


7-1 
8.04 


4.91 
5-79 


60.5 
60.37 


103-75 
104. 1 


86.25 
98 




525 
533 


None. 


55 


96.18 


xk 


5.8 


30 


16 


9-37 


6-73 


59-5 


102.34 


135-5 




619 




54 


96.31 


il 


4.45 


30 


26.1 


10.51 


7-7 


60.75 


102.4 


145 




574 






High-pressure 






























jacket only. 

Steam taken 
from jacket to 
steam-chest of 
high-pressure 




























59 
57 


97-97 
97-93 


A 
^ 


10 78 
7.73 


30 
30 


27 
27 


6.72 
8.03 


4.89 
5-87 


59-75 
59-25 


98.42 
94-98 


73 

94-5 


0.475 
0.52 


420 
420 


None. 


58 


97-5 


T% 


7.01 


30 


27 


8.84 


6.82 


60 


95-75 


103-5 


0.475 


418 






cyhnder. Boiler- 






























pressure, 43-44- 
























427 




38 




102.27 


A 


15.8 


30 


27-5 


6.88 


5-11 


50.75 


87-5 


80 


0.66 


None. 






























( Moz. 


91 


Low-pressure 


97-15 


T^ 


10 78 


30 


27 


7.69 


5-83 


47 


94 


66.5 


1-75 


406 


■< suet per 
( hour. 


28 


jacket only. 


106.8 


% 


9.74 


30 


27.8 


8.72 


7-48 


48-4 


85.6 


88.8 


0.7 


380 




23 


Boiler-pressure, 


104-5 


% 


9.14 


30 


27.2 


9.02 


7-31 


49-75 


101.25 


68.25 


0.62 


388 




35 


40 to 41 pds. 


101.3 


TS 


8.38 


30 


27.6 


9.82 


8.1 


51-5 


92-5 


92-5 


0.64 


383 


Suet. 


30 




no. 2 


14 


7.54 


30 


27-5 


10.94 


8.82 


48 


97-3 


85-5 


0.69 


385 




31 




106.4 


^ 


7.18 


30 


27.7 


11.44 


10. II 


51-5 


97-23 


101.75 


0-77 


407 




32 




99 


H 


5.38 


30 


27.8 


12.39 


10.89 


52 


92.6 


130.5 


0.67 


427 






Steam passed 






















41 


through low- 


93-32 


14 


13.1 


30 


27.1 


6-5 


4.67 


52-37 


92.18 


56.75 


0.4 


347 


None. 


40 


pressure jacket, 


103.4 


M 


13 1 


30 


26.9 




01 


5-t7 


54 


94-5 


60.25 


0.56 


348 


Suet. 


44 


thence to high- 


89.39 


TS 


8.38 


30 


26.8 


8 


85 


6.88 


57-37 


101.78 


74-75 


0.23 


375 


None. 


45 


pressure jacket. 


99-35 


% 


9.14 


30 


26.7 


9 


05 


6.95 


57-37 


102.72 


73-25 


0.61 


367 




46 


thence to valve- 


99.19 


^ 


7.54 


30 


26.9 


9 


08 


6.94 


57-25 


99 


82.5 


0.7 


372 




48 


chest of high- 


97-77 


IS 


6.7 


30 


26.6 


10 


53 


8.80 


58 


100.2 


95-75 


0.64 


385 




42 pressure jacket. 


97.6 


i 


5.8 


30 


27.2 


II 


82 


9.76 


53-25 


89-85 


130.65 


0.61 


405 




49 


Boiler-pressure, 
41 to 45 pds. 


97 S 


% 


4.64 


30 


26.6 


12 


87 


10.7 


58.12 


100.9 


123-5 


0.67 


410 




129 


Throttling ex- 


97-25 


ft 


8.38 


30 


27.25 


8 


65 


6.81 


62.5 


93-1 


108.06 


0.64 


382 


^ oz. suet 




periments. 


























per hour. 


131 


Steam taken 


96.2 


TS 


8.38 


30 


27-5 


9.22 


6.73 


60.25 


95-23 


105-33 


0.62^ 


394 


" 


127 


through low- 


96.8 


^ 


7.73 


30 


27.25 


9-25 


6-77 


62.25 


96.87 


103.52 


0.67 


384 


" 


135 pressure jacket 


96.9 


t's 


15.8 


30 


27 


5-79 


3.88 


59-75 


94-7 


68.4 


0.51 


413 


" 


128 to high-pressure 


102 


None. 




30 


26.4 


6.16 


4.01 


62.37 


103.12 


68.56 


0.58 


453 


" 


132; steam-chest. 


100.3 


" 




30 


26.75 


6.23 


4.01 


61.25 


102.6 


65-5 


0.50 


437 


" 


130 Boiler-pressure, 


101.2 


" 




30 


27.12 


6.06 


4-os 


60.75 


104.6 


61.37 


0.42 


444 


" 


134 


40 to 42 pds. 


103.13 






30 


27 


5 


94 


4.12 


58.0 


95-03 


72.2 


0-45 


450 





342 THERMODYNAMICS OF THE STEAM-ENGINE. 

the indicated horse-power as abscissae and with the number of 
thermal units per horse-power per minute, carried away by the 
condensing water, as ordinates. These curves show in a most 
striking manner the action of steam-jackets on this engine. 

In the course of the tests it was found that if an excessive 
amount of melted suet was fed into the cylinder it formed a 
non-conducting coat on the wall, and lessened the action of the 
walls on the steam. Two sets of experiments were made to 
determine the extent of this effect : in the first, steam was let 
into the high-pressure jacket only, and suet was fed into the 
high-pressure steam-chest at regular intervals ; in the second 
set neither jacket was supplied with steam, and suet was fed 
into the high-pressure steam-chest. The data and results of 
these tests are shown in Table XX, together with the data and 
results of tests made by feeding water into the low-pressure 
cylinder. The results of feeding in suet are also shown by 



X104 




mean ^,^ go 

of two^*>ft^Xv94 Low„88 Pressure Jacket 



Fig. 63. 

Fig. 63, in which the abscissae are ounces of suet fed per hour, 
and the ordinates are thermal units per horse-power per minute 
carried away by the condensing water. 

The importance of these experiments on feeding suet and 
on feeding water nito the cylinders of the engine is connected 
with the question as to the influence of the walls of the cylin- 
der on the steam, and especially with the question as to 
whether the initial condensation, re-evaporation, and exhaust 



VARIOUS STEAM-ENGINE TESTS. 



343 



TABLE XX. 

Tests on Donkin Engine. 







i 

9 


I 




V 




Horse- 




c 

a 


Lubricant. 




la 




Conditions of 


c 

a 

u 




C 
,0 

G 

.2 


a 
— 3 


V 


power. 








c«^a 


^^ 






§ 


1^ 


^^ 








2^ 

ii 




the Test. 


in 

a 

3 

> 


= 
3 y 


11 

_^ 

11 


ii 

^6 


i 

•a 


OS 


ll 


■5 ^ 

3 


•6 
3 

a 


c 

3 


•^a 






^ 


u 


Pi 


Q 


> 


m 


H 


w 





c "^ 


fS 


H 


95 

92 1 

93 f 

901 

911 
96 1 




96.93 


TB 


7-9 


30 


26.75 


9-47 


6.78 


0-IS3 


441 


None. 


.... 




.... 




Suet fed into 


104.47 


Vz 


7-73 


30 


26.37 


9.70 


7-31 


0.165 


412 


Suet. 


0.5 


2% 






hig-h-pressure 






























steam-chest in 






























varying quanti- 




i ^- 


) 


30 i 
















I r, 






97^ 

98 1 

99 1 
101 J 


ties at regular 
intervals. Lovsr- 
pressure jacket 


96.76 


It's 


\\ 


27.25 


8.68 


6.46 


0.112 


412 


(i 


0.75 


]r 




.... 


only. Boiler- 






























89 


pressure, 40 to 
44 pounds. 


97.27 


TS 


10.78 


15 


27.25 


7.48 


5-84 


0.153 


406 


" 


1.50 


5 


.... 


.... 


94 


103.46 


% 


9-74 


30 


26.4 


9-37 


7.24:0.162 


402 


" 


1-7 


I 


.... 




88 




97-43 


TB 


10.78 


15 


27.25 


7-45 


5.85 


0.215 


402 


" 


3- 


2^ 




.... 




Suet fed into 
































high-pressure 
































steam-chest in 






























104 


varying quanti- 
ties and at regu- 
lar intervals. 


96.5 


% 


4-7 


20 


27.25 


10.79 


6.75 





593 


None. 




.. 




.... 


102 


96-5 


% 


6.4 


15 


27-5 


8.84 


6-75 




532 


Suet. 
J Lard 
1 oil. 
Russian 
tallow. 


0:3 

fo.5 

0.7 


5 


— 





108 


Air in both 


94-7 


% 


6.4 


15 


27-3 


9-47 


6.63 




500 


2^ 




.... 


109 


jackets. Boiler- 
pressure, 43 to 

44 pounds. 
In tests 106 and 


96-53 


% 


6.15 


15 


27.22 


9.70 


6.76 




507 


2j^ 


.... 


.... 


100 


96.7 


TS 


6.7 


30 


27.28 


9-31 


6.77 




483 


Suet. 


2 





.... 


103 
106 
107 


107 suet was 
fed through 
grease-cock, in 
106 to h. p. cy- 
linder, in 107 to 
both cylinders. 


96.7 

96-55 

97-6 


I 


6.4 

7.36 

7-36 


15 
20 
15 


27-5 

27-35 

27.4 


8.46 
8.79 
8.5 


6.83 
6.76 
6.83 




476 
449 
433 


" 


6.' 

12. 


I 


:... 


.... 




Water was run 
































continually into 
































the grease-cock 
































on low-pressure 






























116 


cylinder, from 




V2 


7-54 


20 


26.1 


9-63 


6.7 


0.05 


405 


Suet. 


M 




None. 




117 


which it was 






6.8 


15 


25- 


9-23 


6.71 0.09 


502 






% 




0.55 


150 


118 


drawn into the 




M 


5-38 


20 


27. 


9.81 


6.79 . ... 


504 










None. 




121 


cylinder at 




M 


5.38 


20 


25-75 


8.88 


5. 841. .-. 


571 






1 




0.4 


199 


119 


varying rates. 




% 


4-5 


20 I26.5 


10.05 


6.78 




559 








0-5 


145 


125 


In tests 116 and 




t1 


5-0 


10 |25.2 


9.04 


5-84 




564 






% 




0.56 


56 


124 


117, steam was 




% 


4-7 


15 255 


9-23 


5.8 




645 






None. 




1.4 


203 


128 


in the low-pres- 
sure jacket, but 
in other tests 
was in neither 




H 


5-0 


15 


25-5 


8.84 


5.81 




628 




H 




1.6 


204 




jacket. 

































344 THERMODYNAMICS OF THE STEAM-ENGINE, 

waste are caused by the action of the metal of the cylinder or 
of water remaining permanently in the cylinder. 

To further illustrate this method of testing engines, the 
summary of results of two other tests are inserted. One test 
was on a mill-engine, and the other on an engine geared to 
pumps that worked at a slower speed than the engine. 

Both engines were similar to the small experimental engine 
already described. The two cylinders are placed in a line with 
each other, the high-pressure cylinder being situated next the 
crank-shaft. The low-pressure cyHnder only is jacketed, and 
the steam is led through this jacket on its way to the valve- 
chest of the high-pressure cylinder, while the water arising 
from condensation is carried off by an efficient steam-trap. 
The distribution of the steam is effected by ordinary slide- 
valves, that of the high-pressure cylinder having an adjustable 
expansion-valve at the back. The two main valves are driven 
by a single eccentric, the spindle for the low-pressure valve 
being a prolongation of that for the high-pressure cylinder, 
while a second eccentric drives the expansion-valve as usuaL 
The steam passages are all so arranged that the cylinders are 
completely drained. The engine is provided with an ordinary 
injection condenser, and the injection-water is drawn from an 
adjacent river, no cold-water pump being used. 

One engine^ is used to drive rag engines at a large paper- 
mill, and the other f is geared to pumps driven at a slower 
speed than the engine. 

Tests on Donkin Mill-engine. — The object of the test 
was to ascertain the average horse-power, the quantities of coal 
and water used, and to account satisfactorily for all of the heat 
furnished to the engine. 

The feed-water was measured by two cylindrical cans into a 
cast-iron tank ; the level of water in the tank was the same at 
the beginning and end of the test. The temperature of the 
feed-water was taken every twenty minutes. 

Before the experiment commenced all coals were cleared 

* Engineering, November 3, 1871. 

f Proceedings of Civ. Engrs., vol. Ixvi. 



VARIOUS STEAM-ENGINE TESTS. 345 

away from the front of the boiler, and into the space thus made 
the coal to be used on the trial was weighed. The coal used 
was Powell's Duffryn, and was of excellent quality. 

In commencing the experiment at 9.30 A.M., on a signal 
being given- from the engine-house the water-level in the boiler 
was marked on a scale fixed to the glass of the water-gauge, 
the pressure of steam was noted, and both fires were at once 
drawn, with the exception of about a shovelful left in each 
furnace for relighting. About 12 lbs. of wood were then 
thrown in, and the firing commenced with the weighed coal, 
the drawn fires being cleared away. When the fires were 
drawn the steam stood at 50 lbs. per square inch ; in five min- 
utes it had fallen to 49 lbs. ; but in fifteen minutes it had risen 
again to 49I- lbs., and in twenty-five minutes it was at 54 lbs. 
During the day it was kept almost constantly at 53 lbs., 
scarcely ever varying from this pressure more than a couple of 
pounds, and the mean of forty-nine observations taken at 
intervals of twelve minutes showed the pressure last mentioned 
to be the average throughout the experiment. 

At 6.45 P.M., when the experiment was approaching a close, 
the pressure was Si-J- lbs., while at the end of the trial it was 
49f lbs., or almost exactly the same as it was at the beginning, 
while the water-level was also precisely the same. On notice 
being given from the engine-house that the trial was completed, 
both fires were drawn, and the coal, cinders, etc., taken out 
and set on one side to cool, while at the same time the ash-pits 
were cleaned out. When cool, the materials drawn from the 
fires were passed over a sieve with J-inch meshes, and the 
clinkers picked out by hand, and the weight was then found to 
be as follows : 

Cinders, siftings, clinkers, dirt from ash-pit, 2 cwt. 3 qrs. 
20 lbs. 

The total amount of coal charged into the furnaces during 
the trial was 12 cwt., and the quantity consumed was thus 9 
cwt. o qrs. 8 lbs. = 1016 lbs. plus its proper proportion of the 
dirt. Of the siftings, one half was judged to be good fuel and 
the other half dirt, and the total quantity of dirt was thus 13 



346 THERMODYNAMICS OF THE STEAM-ENGINE, 

lbs. siftings -|- lo lbs. clinkers +53 lbs. from ash-pit = "j^ lbs. in 
all, or almost exactly 5.66 per cent. Of this J^y lbs. of dirt, 12 
lbs. (a quantity rather below the proper percentage) was taken 
as belonging to the 239 lbs. of cinders drawn from the fire, and 
the remainder, 64 lbs., was added to the fuel actually con- 
sumed, thus raising the latter to 1080 lbs. 

The quantity of water fed into the boiler during the trial 
was 11,691 lbs., and the evaporation therefore took place at 
the rate of VWV ^^ 10.82 lbs. of water per pound of coal. 

The observations made in the engine-house were as follows: 
I. Every half-hour indicator-diagrams were taken simultane- 
ously from both ends of both cyHnders by means of four Rich- 
ards indicators ; 2. Half-hourly readings were taken of the in- 
dications of the steam and vacuum gauges, and of the counter 
with which the engine was provided ; 3. An account was kept 
of the temperature and quantity of water drawn from the 
steam-jacket ; and 4. Observations were taken every quarter 
of an hour of the quantity and temperature of the water pass- 
ing off from the condenser. The water discharged by the air- 
pump was led along a short iron trough fitted with partitions 
which extended nearly across it. The water on its way down 
the trough was caused to pass under and over and around the 
ends of these partitions, and it was thus thoroughly mingled, 
and the temperature rendered uniform throughout. After 
escaping the partitions it was discharged over a tumbling bay 
having a notch 6 in. wide carefully cut in a brass plate, while 
the head or height of water over the notch was taken by means 
of a hook gauge. The temperature was taken by a delicate 
thermometer, on which the water fell in the tumbling bay. 
The temperature of the water used for injection was also noted 
at frequent intervals during the day, and thus the rise of tem- 
perature in passing through the condenser could be ascertained. 

Test of Donkin Compound Mill-engine. 

Duration of trial: from 9.30 a.m. to 7.30 p.m., = 10 hours. 

Mean pressure of steam in boiler-house, . . , 53 lbs. 

Mean vacuum 27^ in. 

Mean speed of engine 1n revolutions per minute -1651 



VARIOUS STEAM-ENGINE TESTS. 347 

Indicated horse-power — mean results of 84 diagrams: 

Mean indicated power developed in high-pressure cylinder, 32.03 I. H. P. 

Mean indicated power developed in low-pressure cylinder, 24.85 

Mean total indicated horse-power, 56.88 

Observations of water from condenser: 
Temperatures: 

Mean initial temperature of injection-water, Si°.66 

Temperature of water discharged from condenser, . . . 83°. 32 

Rise of temperature in condenser, 31.66 

Quaeitities: 

Mean head over tumbling bay 6 in. wide, taken by a hook- 
gauge, 2y'^ in. bare. 

Mean discharge per minute, 606.5 lbs. 

Pound-degrees: 

Pound-degrees of heat discharged from condenser per 

minute = 606.5 X 31.66, 19,202 

Pound- degrees per indicated horse-power per minute 
19,202 

=16:88-= 337.6 

Water from trap of steam-jacket: 

Total quantity discharged during ten hours, 1,020 lbs. 

Quantity discharged per hour, 102 " 

Feed-water: 

Initial temperature, 61°. 75 

Quantity evaporated during ten hours = 108 cans, weigh- 
ing each io8i pounds = 11,691 lbs. ] 

Quantity evaporated per hour, 1,169.1*' 

Quantity evaporated per indicated horse-power per hour, 20.55 " 

Quantity evaporated per pound of coal consumed, .... 10.82 " 

Coal: Description — Powell's Duffryn: 

Quantity consumed during ten hours, 1,080 lbs. 

Quantity consumed per square foot of fire-grate per hour, 3.27 " 

Quantity consumed per indicated horse-power per hour, . 1.9 ** 

Test on Donkin Pumping-engine. — In the tests on this 

engine, in addition to the determination of the efficiency, it 

was desired to distinguish between the efficiency of the boiler, 
that of the engine, and that of the pumps. The method of 
making the tests was similar to that already described for the 

mill engine. In this test also the feed-water was measured in 

cans, and the condensed water from the jacket on the low- 
pressure cylinder, through which the steam passed on the way 



348 THERMODYNAMICS OF THE STEAM-ENGINE. 

from the high- to the low-pressure cyUnder, was also measured 
in cans. 

The engine drove, through gearing, two sets of pumps, one 
of which lifted water from a well into a tank, and the other 
forced water from this tank into the delivery main. The in- 
jection-water was taken from this tank, and consequently the 
force-pumps delivered so much less water than the lifting- 
pumps. 

On the 29th of March a separate test was made to deter- 
mine the power required to drive, respectively, the engine and 
gearing only, and the engine, gearing, and lifting pumps. The 
distribution of power was found to be — 

Engine and gearing, 12.15 horse-power. 

Lifting pumps, 39-31 " 

Forcing pumps, 35-57 " 



Total, 87.03 " 

The test was continuous, but the calculation has been made 
for the first five hours and the second five hours, as well as for 
the entire run of ten hours. 

TABLE XXI. 

Test on Donkin Pumping Engine. 
April 5, 1881. 

The experiments were made by Messrs, B. Donkin, Jr., Martin, Salter, and 
Bacon. 

engine. 

Class of engine — compound, condensing, horizontal (low-pressure cylinder 
jacketed). 

Name of maker — Bryan Donkin & Co. 

Diameters of cylinders i6|^| inches and 30 inches: diameter of piston-rods 
2f inches and 4 inches (all from gauges). 

Length of strokes, 3 feet. 

Lubricant used in cylinders — Engelbert's. 

Cylinder lubricated every hour: quantity, about 7 ounces per hour. 

BOILER, 

Class of boiler — Lancashire. 

New in 1872. , 



VARIOUS STEAM-ENGINE TESTS. 



349 



Chief dimensions 25 feet long by 6 feet diameter. Two flues, each 2 feet 
2 inches in diameter. 

Total heating surface, 612 square feet. Boiler and flues clean inside and 
out. 

Grate surface — two grates each 2 feet 2 inches by 6 feet, together 26 square 
feet. 

Blow-off cock tight. Fire doors opened only for firing. Direction of smoke 
— through tubes, under, split along sides to chimney. 

Fires 8 inches thick, stoked ten times each furnace, or every hour. 

Pounds of coal per hour per square foot of heating surface, 0.287. 

Pounds of water per hour per square foot of heating surface, 2.720. 

Temperature of engine-house, 62|° ; temperature of outer air, 40°. 



Pressure of steam in boiler-house lbs. 

Duration of trial, from 9 a.m. to 7 P.M without stop- 
page hrs. 

Vacuum in condenser ins. 

Revolutions per minute. ... 

Total revolutions run 

Indicated H. P. 

Indicated power, high-pressure cylinder 

Indicated power, low-pressure cylinder 

Total Indicated H. P 

Water from Condenser. 

Initial temperature of injection-water deg. 

Temperature of water discharged from air-pump " 

Rise of temperature " 

Mean discharge per minute lbs. 

Thermal units per Indicated H. P. per minute 

Water from Steam-jacket. 

Total quantity discharged during ten hours lbs. 

Quantity discharged per hour " 

" per Indicated H. P. per hour. , " 

Feed-water. 

Temperature deg. 

Quantity evaporated during ten hours lbs. 

Quantity evaporated per hour " 

Quantity evaporated per I. H. P. per hour " 

Quantity evaporated per lb. of coal consumed, 
from 85° " 



Ten 
hours. 



52 

10 

27i 

55.25 
33,148 



46.36 
40.67 



First 
five hours. 



87.03 



54.25 
85.06 



30.81 



857 
303 



1,365 

136^ 

1.56 



85 
16,731 

. 1,673 
19.22 

9.52 



52i 

5 

27i 
57-35 
17^205 



48.55 
42.66 



91.21 



54.25 
86.27 



32.02 



865 
303 



710 

142 



84.9 
8,802 
1,760 
19.30 



Second 

five 
hours. 



5 If 

5 

27i 
53.14 
I5>943 



44.17 
38.68 



52.85 



54.25 
83.85 



29.60 



849 
303 



655 
131 



85.1 

7,929 
1,586 
19.14 



3 so THERMODYNAMICS OF THE STEAM-ENGINE. 

The feed-water was measured in a can holding exactly lOO lbs. (special 
standard) at 80°. 

Coal. 

Fires drawn at beginning and end, and 28 lbs. of wood used for lighting up^ 
14 lbs. each fire. 

1,792 lbs. put on fires, less 35 lbs. (= half of large cinders drawn from 
fires) — 

Lbs. 

Quantity used during ten hours, i,757 

" " per Square foot of fire-grate per hour, . 6f 

" " per indicated H. P. per hour, .... 2.02 



Weight of dirt and refuse not burnt Q4i lbs. small cin- ) , 

J I 11-1 -J I I lu 1- 1 Y T45t = 8J percent, 

ders -|- 35 lbs. large cinders -j- 16 lbs. clinkers = ) ^ 

Length of steam-pipe, 55 feet, all covered. Steam-pipes all tight. 
All feed-pipes visible and tight. 



RESULTS AND EFFICIENCY OF THE WATER-PUMPS, AND COM- 
PARISON OF THE CONTENTS OF THE PUMPS WITH THE 
WATER PUMPED. 

Three Deep-well or Lower Pumps. 

Dimensions and calculated contents: 

Pumps 14 inches diameter, mean stroke 2 feet 8f inches. 

Contents of these three pumps 8.755 cubic feet — 546.3 lbs. per revolution. 

Mean speed for ten hours = 12.174 revolutions per minute. 

Contents per minute = 6,651 lbs. 
Quantity actually pumped: 

Mean height over 2 feet 3 inches bay in engine-house = 4.395 inches. 

Temperature of water 54°. 

Quantity = 6,183 lbs. per minute. 
Efficiency: 

6,183 -!- 6,651 = 93 per cent water lifted of theoretical contents. 

Three Force or Upper Pumps. 

Dimensions and calculated contents: 

Pumps, 12 inches diameter. Strokes, two 2 feet i| inch, one 2 feet 2 inches. 

Contents of these three pumps 5.09 cubic feet = 317.6 lbs. per revolution. 

Mean speed for ten hours = 20.819 revolutions per minute. 

Contents per minute = 6,612 lbs. 
Quantity actually pumped: 

Same as lower pumps (6,183 lbs.) less 831 lbs. used for injection = 5,352 lbs. 
Efficiency: 

5,352 -7- 6,612 = 81 per cent water lifted of theoretical contents. 



VARIOUS STEAM-ENGINE TESTS. 



351 



Comparison of measurement 
of water in engine-house 
over 2 feet 3 inches bay, 
with that at reservoir over 
two I foot 6 inches bays. 



Inches. 
Engine-house, 4.38 height = 
Reservoir, 3.38 

3-27 
Add injection (water) 



Lbs. 
6,155 



h 



5,421 

831 



For about eight hours. J Leak of rising main (measured) 10 6,262 

The latter i^ per cent more nominally than the 
former. 

Percentage of foot-pounds of ^ Lbs. Feet. H. P. Foot-lbs. 

water lifted, of foot-pounds [-Lower pumps, 6,183 198 lift = 37.1 (of 33,000) 
of steam-pistons. ) Upper " 5,352 148 " =24,1 61.2 H. P. 



Steam-pistons, 87.03 " 

Foot-pounds of water lifted, per cent of foot- 
pounds steam-pistons, 70. 
Average velocity of water in rising main, 1.3 foot per second. 



HEAT ACCOUNT OF THE STEAM-ENGINE IN THERMAL UNITS 
OR POUND-DEGREES PER MINUTE. 





Units. 


Per cent. 


Dr. to boiler: 






Feed, 27.888 lbs. X (1,204°. 8 — 85° =) 1,119°. 8 = • • 


3^.229 


.... 


Cr.: 






By power, 87.03 I. H. P. X 42.76 = . 


3,721 


= 11.9 


By waste water from condenser: 






Injection, 831.33 lbs. X (85^.06 — 54^25 =)30°.8i = 25,613 






Condensed 1 t. , „ „ r . 1 
Feed, 27.89 lbs. — water from trap 

. ^^^^"^ y 2.30 lbs. = 25.59 lbs. X (85°.o6 y= 2 
m waste „ x ^0 

-85° =) .06° = 

water. J J 






25,615 


= 82.4 


By water from steam-trap 2.30 lbs. X (212° — 85° =)i27° = 


293 


= 0.9 


By balance unaccounted for, radiation, etc. = . . . . 


1,600 


= 4.8 




31.229 





Major English's Tests. — In November and December, 
1886, tests were made by Major Thomas English, R. E.,* to 
ascertain the most economical method of working some direct- 
acting, high-pressure, fly-wheel pumping-engines, intended for 



* Proceedings of the Inst. M. E. 1887. 



352 THERMODYNAMICS OF THE STEAM-ENGINE. 

use in a hot climate, where fuel was dear, water scarce, and 
where difficulties of transportation prohibited heavy weights. 
The first object of the tests was to determine whether, under 
the circumstances, it was advisable or not to use a surface con- 
denser. The results of the tests shown in Table XXII show 
that the economy of the engine was small and the consumption 
of steam was not satisfactory whether the engine was run con- 
densing or non-condensing. In addition to ascertaining the steam 
consumption. Major English made a very complete analysis of 
the distribution of the heat, as is shown by the table, and for 
this reason the tests are of interest. Each engine consisted of 
a pair of horizontal cylinders, i6 inches diameter by i8 inches 
stroke, lagged, but not jacketed. Each cylinder drives a differ- 
ential pump on the prolongation of the piston-rod, with rams 4 
inches and 5f inches diameter, working up to 700 pounds on 
the square inch. The piston-rods, 2\ inches diameter, pass 
through both ends of the steam-cylinder, and are connected by 
a crank-shaft, which has cranks at right angles and a fly-wheel 
on each end. The engines are sufficiently self-contained to 
work on a foundation of three timbers bolted together with dis- 
tance blocks. Each cylinder has a main or distribution slide- 
valve, and on its back cut-off plates that can be adjusted by 
hand to give different rates of expansion. 

The steam during the tests was furnished by three multi- 
tubular boilers of the locomotive type. Two of these boilers 
were used together to furnish steam for one main engine, an 
air-pump engine and a feed-pump. The surface of the steam- 
pipe leading from the boilers to the engine was 141 square 
feet. During some of the tests this steam-pipe was jacketed 
with steam from a separate boiler at 140 pounds pressure. 

The air-pump and circulating-pump were operated by one 
auxiliary engine with a steam-cylinder 10 inches in diameter by 
14 inches stroke. The feed-pump was a direct-acting Worth- 
ington pump. The steam from these two auxiliary engines 
was condensed in a surface condenser, collected, and weighed. 
The exhaust from the main engine was in all the tests con- 
densed in a tubular surface condenser, collected, and measured 



VARIOUS STEAM-ENGINE TESTS. 353 

in a tank of known capacity. During the non-condensing tests 
the air-pump was disconnected and the exhaust was condensed 
at atmospheric pressure. 

The average evaporation during the tests was 7.9 pounds of 
water per pound of coal ; the rate of combustion varied from 
6.5 to 12.4 pounds per square foot of grate surface per hour. 
No priming worth notice appeared at any time. 

The indicator-diagrams were taken by a Richards indicator 
with a 30 spring. The spring was tested by the makers after 
the tests, and was stated to be correct. The clearance of the 
engine is seven per cent of the piston displacement. 

The data and results of the tests are given in Table XXII, 
which requires little explanation in addition to that given by 
the headings. 

In columns 11, 12, and 13 are given the heat equivalents of 
the total work without allowing for back pressure, the effective 
work, and the work of the back pressure, for each pound of 
steam supplied. 

The distribution of the heat lost at the end of the stroke is 
shown by columns 14, 15, and 16, calculated from the condi- 
tion of the steam at release, for each pound of steam supplied. 
The heat in the steam and the water at release is unavoidably 
rejected, but that abstracted by the walls of the cylinder 
corresponds to the exhaust-waste Q^ of Hirn's analysis. 

The thermal unit per pound of steam, column 17, is the 
difference between the total heat of one pound of steam at the 
initial pressure and of the heat of the liquid at the mean back 
pressure. 

The condensation at the end of the stroke is the ratio of the 
weight of dry saturated steam required to fill the cylinder up 
to release, to the actual weight of steam and water then pres- 
ent in the cylinder. 

Column 19 gives the number of thermal units that could be 
converted into work for each pound of steam in a perfect en- 
gine ; obtained by multiplying the heat supplied (column 17), 
by the efficiency of a perfect engine working between the 



354 



THERMODYNAMICS OF THE STEAM-ENGINE. 



TABLE 

Major English's Tests of a 





Conditions of 


2 


i 


u 
to 


Absolute pressures. 





Consumption 
of water. 


1 


h 


Jo V 


0) 

•23 


^.; 


■ - IUJ3 
T3 03 , 





1 

a 




Test. 


o 

1 

a 

o 


o 

a. 2 

a CO 


.2 a; 

3 3 
'o.S 

Sa 


l-s 

•4:! 3 




§£.S 


(J — 






to 
u 


^ 






^ 


iz; 


Pi 


H 


S 


s 




J 


hJ 








1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


1 






J 


3-4 


40.2 


71.3 


22.8 


43.1 


2.9 


57-8 


34.2 


0.205 


2 


c 


SoTiJ 




s.« 


39-5 


89.0 


18.9 


39.4 


3.2 


50-3 


34 -o 


0.182 


8 


S.S-^ 


,S-B 


39.7 


82.6 


17.6 


36.1 


3-2 


46.6 


36.1 


0.176 


4 


c 


^"^S 




5-8 


40.4 


83-3 


19.3 


38.0 


4.2 


49.4 


38.2 


0.194. 


5 


^ 


6.7 ' 


40.9 


87.4 


17.0 


35.0 


2.7 


46.9 


34.6 


0.165 


6 


kol 


\ 


3-4 


42.2 


72.6 


23.5 


44.1 


2.6 


62.0 


35-4 


0.217 


7 




k 


^.ii 


40.3 


86.5 


18.7 


38.0 


2.5 


51-0 


34-7 


0.183 


8 




ijt«o 


k 


S.8 


40.4 


83.3 


17.7 


36.1 


3-3 


47.2 


38-9 


0.190 


9 




c/5«- .rt 


tV 


6.7 


41.2 


86.8 


16.0 


33.5 


2.4 


45-7 


38.8 


0.179 


10 


, 


fl -2 


I 


3-4 


40.4 


83.7 


28.8 


51.8 


15-4 


52-4 


39-6 


0.214 


11 


H 


\ 


5.8 


40.1 


90.9 


22.3 


41.7 


16., S 


36.2 


41.2 


0.155 


12 


tj 


5i-a" 


^s 


6.7 


40.1 


88.1 


20.0 


36.8 


16.2 


29.6 


42.9 


0.132 


13 


II 


^"".^ 


15 


6.7 


39-3 


87.8 


20.2 


36.6 


15.5 


29.6 


5I-0 


0.160 


14 


i^o^-S 


^ 


3-4 


39-8 


87.6 


28.1 


52.6 


16.6 


51.0 


^i.i 


0.220 


15 


^ 


I 


5.8 


40-3 


91.6 


21.9 


41.8 


16.7 


36.0 


42.6 


0.158 


16 


cg-^5,ti 


^ 


6.7 


39-5 


89.3 


20.0 


36.7 


15.6 


29.7 


50.5 


0.158 



initial temperature and the temperature due to the back 
pressure. 

The absolute efficiency, column 20, is the ratio of the heat 
changed into work to the heat supplied; column 12 and col- 
umn 17. 

The ratio of the efficiencies of the actual engine and of a 
perfect engine (column 21) is the ratio of the heat changed 
into Avork in the actual engine (column 12), and the heat 
changed into work by a perfect engine (column 19). 

Major English gives also diagrams representing the distri- 
bution of heat for each of the tests stated in the table. The 
diagrams are reproduced in Figs. 64 and 65, for the 6th and 
14th tests. 

The upper part of the figure gives the maximum and 
minimum diagram taken during the test, with a few inter- 
mediate diagrams. The axes are obtained by laying off the 



VARIOUS STEAM-ENGINE TESTS. 



355 



XXII. 

Stationary Steam-engine. 



s 


Ha 

"15 S 




Thermal units of 

heat lost at end of 

stroke. 






al work of perfect 
gine, thermal units 
r lb. of steam sup- 
ed. 




go; 


;ncy of 
e in per- 
fficiency 
gine. 


XI . 










'5 . 

la 


II 

•0 "> 


|3 


.= c <u c 


Ill 




si 




> ni rt <u 


Jtt E«5 






m ^ 




U 3 


^'v. 


*-: c <u'^ 






rt- 


><^ 


.. 


^X1T3 


JZ W3 





u ao- 




(u oi (J 


H 


W 


P3 


w 


< 


H 


u 


H 


<: 


Di 


11 


12 


13 


14 


15 


16 


17 


18 


19 


20 


21 


8o 


75 


5 


590 


38 


359 


1067 


39-3 


244 


7.0 


30.8 


82 


75 


7 


543 


36 


407 


1068 


43-7 


240 


7.0 


31-3 


78 


71 


7 


52b 


35 


427 


iu66 


45-5 


233 


6.7 


30-5 


75 


66 


9 


521 


32 


427 


1055 


45-5 


217 


6.3 


30-5 


80 


74 


6 


550 


35 


407 


1072 


43-3 


249 


6.8 


29-3 


77 


72 


5 


567 


43 


384 


1071 


41.9 


237 


6.7 


30-3 


79 


72 


7 


544 


40 


412 


1075 


44.1 


252 


6.6 


28.2 


72 


65 


7 


489 


37 


467 


1065 


49.2 


233 


6.1 


28.0 


71 


65 


5 


482 


42 


482 


1077 


50-5 


254 


6.1 


25.6 


92 


65 


27 


613 


II 


279 


995 


31-8 


129 


6.5 


49.6 


103 


63 


40 


650 


5 


23s 


993 


27.2 


131 


64 


48.1 


107 


61 


46 


684 


3 


199 


993 


23-3 


129 


6.1 


47.2 


87 


51 


36 


571 


5 


332 


995 


36.1 


131 


5-1 


39-0 


/ 91 


62 


29 


581 


10 


310 


992 


35-1 


127 


6.2 


48.8 


100 


61 


39 


621 


4 


269 


994 


30-4 


131 


6.1 


45.8 


88 


51 


37 


573 


5 


330 


996 


35-9 


134 


5-1 


38.1 



vacuum line at the proper distance below the atmospheric 
line, and by laying off the line of zero volume, allowing 
for clearance. The entire volume, including clearance, is 
divided into ten equal parts, and ordinates are drawn upon 
which the absolute pressures are measured to points shown 
by dots on the ordinates. In the lower part of the figure 
the total height represents the total thermal units supplied, 
column 17, Table XXII. The curve EE represents the ther- 
mal units per pound of steam, changed into work, obtained 
from the area of the indicated diagram to the left of the 
ordinate in question. The line TT is obtained by adding to 
the heat changed into effective work the heat per pound of 
steam required to do the work of the back pressure, which is 
obtained from the area below the back-pressure line and to the 
left of the ordinate. The line TT, therefore, represents at 
each ordinate the heat per pound of steam required to do the 



356 



THERMODYNAMICS OF THE STEAM-ENGINE. 



absolute work up to that point of the stroke of the engine. 
To obtain the hne 55, the fraction x, of a pound of the mixture 
in the cyHnder which was 5team, was calculated for each ordi- 
nate, from the volume and pressure, and the heat in that steam 
was calculated by the expression 

in which r and q are the heat of vaporization and the heat of 
the liquid corresponding to the pressure measured on the ordi- 



„0 Volume of Cylinder 1 including' clearance 2 




lu 20 30 40 50 60 70 8o 90 100 
Percentage of stroke including clearance 

Fig. 64. 



lu 20 30 40 ,50 60 70 ou au 

Percentage of stroke including clearance 

Fig. 65. 



nate, and q^ is the heat of the liquid corresponding to the back 
pressure. The number of thermal units was then plotted on each 
ordinate from the line TT, so that the line 55 represents the 
heat per pound of steam, changed into work, plus the heat re- 
maining in the steam. A similar calculation was made for the 



VARIOUS STEAM-ENGINE TESTS. 357 

fraction of a pound of the mixture at each ordinate that was 
water, using the expression 

(l _ x){q - q,), 

and the Hne WW \YdiS plotted by laying off the quantities thus 
found from the line 55 ; so that the hne WW represents the 
heat per pound of steam, changed into work, plus the heat 
remaining in the water and«steam. The portion of the total 
heat received per pound of steam, above the line WW, repre- 
sents the heat absorbed by the walls of the cylinder ; this 
quantity diminishes as the expansion proceeds on account of 
the re-evaporation. 

The dotted curve PP represents the heat theoretically 
necessary to do the total work shown by the curve TT. 

A comparison of all the observed results is shown by Fig. 
000, in which the abscissae represent square feet of surface 
exposed to the steam throughout the stroke by the steam- 
passages, cylinder, and piston ; the clearance surface measures 
5.24 square feet at the commencement, and the total surface 
11.98 square feet at the end of the stroke. Ordinates measured 
downwards from the top of the diagram represent the number 
of thermal units abstracted from the enclosed steam at any 
point ; and the curves are plotted from such ordinates for each 
point of the stroke. The palpable convergence of all of these 
curves to the zero of exposed surface at about 150 thermal 
units agrees closely with the hypothesis that there is a sudden 
initial condensation of steam, equivalent, in all the tests on this 
engine, to the transference of 150 thermal units, or 28.6 thermal 
units per square foot of exposed clearance surface, to the metal 
surface of steam-passages, cylinder, and piston ; and that this 
heat is gradually given back again to the steam during the 
stroke, by re-evaporation. The heat thus regained increases 
approximately in proportion to the surface exposed ; but 
still leaves in the metal, at the end of the stroke in this engine, 
an amount of heat equivalent to 0.4 thermal unit for each de- 



358 



THERMODYNAMICS OF THE STEAM-ENGINE. 



gree of difference between the temperatures corresponding to 
the initial and back pressures. 

By the aid of this hypothesis the heat abstracted by the 
walls of the cylinder at each point of the stroke of the piston 
has been calculated, and is represented by the line AA on the 
Figs. 64 and 65. By the same hypothesis the diagrams rep- 



Initial Conde-vsation and Re-evaporation 
Percentage of Stroke 10 20 30 40 50 60 70 80 90 100, 
























10 

20 
30 
40 
50 












































/ 




















/ 


/ 
/ 
















/ 


/ 


/ 


/ 












/ 


/ 


/ 


'/ 


/ 


Y 










/ 


t 


^ 


/ 


// 


</ 


V. 


70 


Condensing J£\il"£~:2 
Noncondensing 






/ 




'/ 


/ 


y 




V. 


rj 










^ 


^ 


V 


4^'^ .y 












^ 


^w 


/ 


100 
110 
120 








r 


■P^ 


s 
















'? 


^ 


' 


































( Clearance Surf ace 
'■including cylinder-end V> 
( and piston-face 


*Si 


irfi 


ice 


o, 


Sid 


es 


)f( 


;yi 


nd 


er> 




1 1 \ i r^ 






















150 



01234567 89 10 U 11-98 
Square feet of Surface exposed to Steam 

Fig. 66. 



resented by the dotted lines in the upper part of Figs. 64 and 
65 have been deduced by the reversal of the processes used 
in laying out the lines EE to WW. The following table ex- 
hibits the correspondence between actual observed quantities, 
and quantities calculated on this hypothesis. 



VARIOUS STEAM-ENGINE TESTS, 



359 



Indicated horse-power. 

Water per stroke 

Efl&ciency, per cent... 



Experi 


ment 6. 


Experiment 14. 


Observed. 


Calculated. 


Observed. 


Calculated. 


62.0 
0.217 
6.7 


65.6 
0.2II 

7.8 


51.0 
0.220 
6.2 


57.1 
0.209 
7.6 



Major English draws the following conclusions from the 
tests : 

In order to obtain the best results for any given range of 
temperature there should be a definite relation between the 
surface of the steam-passages, the diameter of the cylinder and 
the length of the stroke ; and that in the design of an engine 
the adjustment of these proportions may be the most impor- 
tant item affecting economy. The following table shows for 
two different points of cut-off the calculated results of varying 
the length of the stroke of the engine experimented on, while 
the diameter of the cylinder, the absolute clearance volume 
and the clearance surface exposed, remain unaltered ; and it 
will be seen that the same number of expansions may give 
widely different results as regards the ratio of efificiency and 
the water consumed per indicated horse-power per hour ; and 
also that, with the same length of stroke, these results are but 
slightly affected by doubhng the number of expansions. 

Calculated Efficiency and Consumption of Steam with varying 
Length of Stroke. 



Diameter of cylinder, 16 inches. 
Clearance, 0.143 cubic feet. 
Clearance surface, 5.24 square feet. 



Length of stroke, inches. 
Number of expansions 



Percentage of efficiency 

Steam per ind. h. p. per hour, pounds. 



Cut-off, 1.4 inch. 
Absolute initial 

pressure, 87.4 pds. 
Bac k pressure , 2.7 

pounds. 



8.0 

3-47 



4.8 
56.0 



18.0 

7.24 



7-3 
34-6 



8.67 



8.1 
31-3 



Cut-off, 4.25 inches. 
Absolute initial pressure, 

pounds. 
Back pressure, 2.9 pounds. 



71-3 



8.0 

1.68 


18.0 
3-47 


21.8 
4.20 


38.6 
7.24 


5-3 
54.8 


7-9 
32-5 


8.6 
30.0 


10.3 
23.0 



46.3 
8.67 



Initial Condensation. — Subsequently to the preceding 
steam-engine tests Major English * made some important experi- 
ments to determine the amount of initial condensation directly. 



* Proceedings of the Inst, of M. E. 1887. 



360 THERMODYNAMICS OF THE STEAM-ENGINE. 

The experiments were made on a portable engine, 10 inches 
diameter and 14 inches stroke, jacketed on the sides, but not on 
the ends. The connecting-rod was disconnected, the piston 
was rigidly blocked at the end of the cylinder farthest from 
the crank, and the interior of the cylinder was completely 
filled with wood and iron, as was also the steam-passage at 
the crank end. The port at the crank end was filled with a 
brass plate scraped down to a level with the valve-seat. The 
port at the head end was left open, and the crank-shaft, 
eccentric, and valve were driven by another engine. The steam- 
pressure in the boiler was maintained uniform during a trial, 
and the regulator was kept open. As a consequence, steam at 
boiler-pressure was alternately admitted to and exhausted 
from the clearance space at the head end, once each revolution, 
for a time corresponding to a cut-off at seven tenths of the 
stroke. 

Each experiment lasted an hour, during which time revolu- 
tions were noted by a counter, and indicator-cards were taken. 
The steam passing through the engine under these conditions 
was condensed, collected, and weighed. Sixty-four satisfactory 
tests were made, of which thirty-five were condensing and 
twenty-nine non-condensing. The steam-pressures were about 
45, 30, 20, and 10 pounds above the atmosphere ; and the num- 
bers of revolutions were 130, 100, 70, and 50 per minute. 

Let y^ be the density or weight in pounds of one cubic 
foot of steam, of the steam up to the point of cut-off, and let 
t^ be the temperature ; let y^ and t^ be similar quantities at the 
time when the exhaust-port closes. 

Let M be the weight of water per revolution from the con- 
denser. This is made up (i) of the differences of the weights 
of steam shown by the indicator at cut-off and compression, 

in which V^ is the volume in cubic feet of the clearance space, 
including the steam-passages; and (2) of the weight of steam 
condensed, and not re-evaporated, on the constant surface S^ 
square feet of the clearance, including the steam-passages. The 



VARIOUS STEAM-ENGINE TESTS. 



361 



weight of steam condensed per revolution and not re-evapo- 
rated is 

^-(r.-r.)^o- 

Let Aj be the total heat of steam at the temperature t^ , and 
let ^1 be the heat of the liquid ; then the thermal units absorbed 
by the clearance surface are 

These several quantities are given in Tables XXIII and 
XXIV. 

TABLE XXIII. 
Initial Condensation in Jacketed Cylinder of Non-condensing Engine. 





Clearance 
volume. 

^0 


Revolu- 
tions 
per 
second. 


Density of steam. 
Lbs. per cubic ft. 


Thermal units in 
one pound of 


Water 
collec'd 

per 
revolu- 
tion. 

M 


Net initial con- 
densation by 
clearance 




Initial. 
7i 


Exhaust. 

Y2 


Steam. 


Water. 


surface. 
Thermal units. 


1887. 


Total 

per 

revolu- 

tion. 

C 


Per sq. 
feet of 
surface 
at one 
rev. per 
second. 

s 


May 16 

May 25 

May 28 

May 13 

June I 

May 16 

June2 

May 13 

May 16 

May 14 

May 25 

May 28 

May 17 

une 2 

une I 

Mayi4 

May 17 

May 25 

Mayi4 

May 31 

; une I 

.une 2 

May 17 

May 25 

May 31 

May 31 

May 14 

May 17 

June 2 


Cubic ft. 
0.035 
0.035 
0.035 • 
0.035 
0.035 
0.035 
0.035 
0.035 
0.035 
0.035 
0.035 
0.035 
0.035 
0.03s 
0.035 
0.035 
0.035 
0.035 
0.035 
0.035 
0.035 
0.035 
0.035 
0.035 
0.035 
0.035 
0.035 
0.035 
0.035 


Revols. 
1-73 
2.19 
1.70 
1.23 
1. 21 
1.64 

m 

1-54 
1.32 
2.09 
1.65 
1.62 
0.85 
1.25 

IM 

2.05 
1.25 
1.69 
1. 19 
0.80 
1. 71 
2.12 
1.65 
1. 19 

\t 

0.85 


Lb. 

0.156 
0.149 
0.148 
0.148 
0.146 
0.146 
0.144 
0.140 
0.126 
0.118 
0.117 
0.116 
0.115 
0.115 
0.113 
0.104 
0.103 
0.095 
0.092 
0.091 
0.090 
0.089 
0.089 
0.071 
0.071 
0.070 
0.068 
0.067 
0.066 


Lb. 

0.043 
0.042 
0.043 
0.043 
0.043 
0.040 
0.042 
0.043 
0.040 
0.041 
0.040 
0.039 
0.042 
0.039 
0.040 
0.041 
0.043 
0.039 
0.040 
0.041 
0.040 
0.040 
0.041 
0.039 
0.040 
0.039 
0.039 
0.040 
0.039 


Units. 
"73 
1172 
1172 
1172 
1171 
1171 
1171 
1170 
1168 
1167 
1166 
1166 
1166 
1 166 
1166 
1165 
1 164 
1163 
1163 
1162 
1162 
1161 
1161 
1157 

1157 
1156 
1156 
1156 
1156 


Units. 
269 
265 
265 
265 
263 
263 
262 
260 
254 
248 
247 
247 
247 
247 
246 
241 
240 
234 
233 
232 
231 
230 
230 
216 

2l6 

214 
213 
212 

212 


Lb. 

0.0213 
0.0135 
0.0160 
0.0240 
0.0237 
0.0161 
0.0251 
0.0170 
0.0147 
0.0150 
0.0098 
0.0154 
0.0150 
0.0225 
0.0128 
0.0120 
0.0149 
0.0069 
0.01 10 
0.0124 

O.OIOI 

0.OI5I 
0.0102 

0.0044 
0.0074 
0.0080 
0.0065 
0.0060 
0.0081 


Units. 

15-7 
8.9 
11.2 
18.4 
18.3 
"•3 
19.6 
12.4 
10.7 
ii-3 
6.5 
11.7 

II-5 

18.2 
9.4 
9.0 

11.8 
4.6 
8.6 
9-9 
7-7 

12.5 

7-9 
3-1 
5-9 
6.4 

5-1 

11 


Units. 

7.1 

7-3 
10.2 
10. 1 
7.2 
9.4 
8.1 
6.1 
6.5 
4-7 
7-5 

1:1 

5-3 

5-2 

7.6 

3-3 
4.8 
6.4 

Ve 

5-2 
2-3 

3-8 
3-5 
3-0 
3-0 
3-1 



3^2 



THERMODYNAMICS OF THE STEAM-ENGINE. 



TABLE XXIV. 
Initial Condensation in Jacketed Cylinder of Condensing Engine. 





Clearance 
volume. 

^0 


Revolu- 
tions 
per 
second. 

N 


Density of steam. 
Lbs. per cubic ft. 


Thermal units in 
one pound of 


Water 

collec'd 

per 

re volu- 
tion. 

M 


Net initial con- 
densation by 
clearance 




Initial. 


Exhaust. 


Steam. 
^1 


Water. 


surface. 
Thermal units. 


1887 


Total 
per 
revolu- 
tion. 

C 


Per sq. 
feet of 
surface 
at one 
rev. per 
second. 

S 


June 13 

June 15 

June 10 

June 16 

Aug. 4 

Aug. 3 

July 28 

July 13 

4^S. II 

Aug. 13 

. une 15 

^ une 13 

.une 16 

Aug- 3 

une 10 

July 13 

Aug. II 

July 28 

Aug. II 

.une 13 

J une 13 

,une 16 

uly 26 

July 28 

Aug. 3 

Aug. 12 

Aug. 12 

June 13 

June 13 

July 26 

July 26 

Aug. 4 

Aug. 12 

Aug. 4 

Aug. II 


Cubic ft. 

0.035 
0.035 
0.035 
0.035 
0.035 
0.03s 
0.038 
0.038 
0.038 
038 
0.035 
0.035 
0.035 
0.035 
0.035 
0.038 
0.038 
0.038 
0.038 
0.035 
0.035 
0.035 
0.038 
0.038 
0.035 
0.038 
0.038 
0.035 
0.035 
0.038 
0.038 
0.03s 
0.038 
0.035 
0.038 


Revols. 
1.69 
1. 21 
1.80 
0.83 
1-95 
0.87 
1.09 
1.60 

1.59 
2.17 
1. 13 
1. 6s 
0.89 
0.85 
1.90 
1. 61 
2.13 

^■\^ 
1.65 

2.09 

1.70 

0.86 

1. 15 

0.81 
2.17 
1. 6s 
2.19 
1.72 
1.16 
0.83 
0.88 
2.13 

I.I3 
1.70 


Lb. 

0.146 
0.145 
0.143 
0.143 
0.143 
0.143 
0.142 
0.140 
0.140 
0.138 
0.118 
0.117 
0.116 
0.114 
0.113 
0.112 

O.III 
O.III 

o.iir 
0.091 
0.091 
0.091 
0.090 

0.087 
0.083 
0.071 
0.070 
0.070 
0.070 
0.066 
0.066 
0.065 
. 063 


Lb. 

0.020 
0.020 
0.024 
0.015 
0.019 
0.012 
0.028 
0.023 
0.018 
0.025 
0.017 
0.019 
0.015 
0.012 
0.019 
0.021 
0.015 
0.025 
0.015 
0.016 
0.016 
0.014 
0.020 
0.017 
0.012 
0.015 
0.018 
0.015 
0.014 
0.015 
0.015 
0.012 
0.014 
0.012 
0.013 


Units, 
1171 
1171 
1171 
1171 
1171 
1171 
1171 
1T70 
1170 
1170 
1167 
1166 
1166 
1166 
1166 
1166 
1165 
1165 
1165 
1161 
1161 
1161 
1161 
1161 
1161 
1161 
1 160 

1157 
1x56 
1156 
1156 
1156 
1156 
1155 
1155 


Units. 
263 
263 
262 
262 
262 
262 
262 
261 
260 
259 
249 
247 
246 
246 
246 
246 
244 
244 
244 
231 
231 
231 
231 
230 
230 
230 
225 
216 
215 
215 
215 
213 
212 
210 
209 


Lb. 

0.0173 
0.0227 
0.0163 
0.0257 
0.0203 
0.0181 
0.0233 
0.0154 
0.0160 
0.0136 
0.0193 
0.0168 
0.0199 
0.0142 
0.0107 
0.0115 
0.0093 
0.0137 
0.0115 
0.0084 
o»oio9 
0.0144 
0.0149 
0.0125 
0.0142 
0.0087 
0.0122 
0.0066 
0.0094 
0.0114 
0.0134 
0.0130 
0.0060 
0.0103 
0.0103 


Units. 
II. 7 
16.6 
II. 
19-3 
14-5 
12.3 

17.3 
10. 
10.6 
8.5 
14. 5 
12.3 

15-1 
9.8 
6.8 
7-4 

%l 

7.3 
5.4 
7.7 
10.9 

II. 3 
9.1 

10.7 
5.6 
9.1 

4.3 
7.0 
8.8 
10.6 
10.5 
3-8 
7.9 
7-9 


Units. 
7.6 
9.1 
7-4 
8.8 
10.2 
5-7 

!;i 

6.3 
7.7 

.7-9 
7-1 
4-5 
4-7 
4.7 
3.8 
5-2 
4.7 
3-9 
5.0 
5.1 
6.1 
4.8 
4.8 
4.1 
5.8 

il 
\l 

4.2 

5-2 



The results of the experiments indicate that the excess of 
initial condensation over re-evaporation, in these experiments, 
varies directly as the initial density and inversely as the square 
root of the number of revolutions iV, per unit of time. Assum- 
ing that it varies also as the surface (2 square feet), the last 



VARIOUS STEAM-ENGINE TESTS, 



363 



column of the tables gives the amount in thermal units for one 
square foot and one revolution per second. The results of the 
experiments are also plotted in Fig. 6j, using thermal units 



0.05 



0:10 



^ 8 
g 



V 



I 

m 



,11 



1 — ^ — i — i ' I I i r- 

Portable Engine, 

worked .with and without 

Condenser. 

With Condenser o 

Without < 



lTo 



'0 0.05 0.10 O.lSLbi, 

Initial Density of Steam, Ib.per Cubic foot, 

divided by square root of revolutions per second. 

Fig. 67. 



per square foot as ordinates and the initial density divided by 
the square root of the number of revolutions for abscissae. 

The average of the whole series of experiments corresponds 
with an excess of condensation over evaporation, equivalent to 
8.2 thermal units per square foot of clearance surface for steam 
at 60 pounds pressure absolute. 

Major English states that these experiments and his exper- 
iments given in Table XXII, and also the experiments on the 
revenue steamers, pages 270, 273, and 276, may be fairly repre- 
sented by the following formulae for the excess of condensation 
over re-evaporg-tion at any point of the stroke of an engine. 



364 THERMODYNAMICS OF THE STEAM-ENGINE. 

For Jacketed Cylinders. 

6or,S, I y, + 0.06 ^> 



{X,^{xr-^q + AW)\M=-^-[i 



For Unjacketed Cylinders. 

M = excess of pounds of water condensed over re-evapo- 
ration ; 
*i;r -{- g = thermal units per pound of the mixture in the cylin- 
der at any given point of the stroke ; 
AW =^ heat equivalent of the work done up to that point ; 

Aj = total heat of steam at cut-off ; 

y^ = density of steam at cut-off ; 

y^ = density of steam at compression ; 

»S — surface of cylinder, including clearance up to the 
given point ; 

Sc — surface of clearance ; 

JV — revolutions. 

Willans' Steam-engine Tests. — In 1887, Mr. Peter 
Willans * made a large number of tests under various circum- 
stances on an engine of peculiar form invented by him. 

This engine is represented by Fig. 68, which gives a verti- 
cal section. It has three single-acting pistons of diminishing 
diameter on a hollow piston-rod, which forms the steam- 
passages and is provided with ports and piston - valves for 
admitting and exhausting steam from the several cylinders. 
The space below each of the two smaller pistons and above 
the head of the next larger cylinder forms a receiver, into 
which the steam is exhausted and from which it is drawn 
by the cylinder below. Below the exhaust space under the 
large piston is a compression chamber filled with air to 
insure a constant compression on the piston-rod. The piston 

* Proceedings Inst. Civ. Eng., vol. xciii. 



VARIOUS STEAM-ENGINE TESTS. 



3^5 



working in this chamber serves also 
connecting-rod, which is made dou- 
ble. The several valves are all on 
one rod in the hollow piston, and 
are moved by an eccentric on the 
crank-pin between the connecting- 
rod ends. The cut-off is effected 
by the ports in the hollow piston- 
rod, running past a ring placed on 
the cylinder-head, at full piston 
speed, and can be varied by hand 
or by a governor. During the 
tests the cut-off was accomplished 
by a fixed ring for each test. 



as the guide to the 



The pressures in the receiver 
spaces between the smallest cylin- Exha 
der and the intermediate cylinder, 
and between the intermediate 
cylinder and the largest cylinder, 
varied to such a degree that there 
were really five stages of expan- 
sion in the engine when running 
nominally with triple expansion, 
and three stages when running 
compound. In Fig. 69 the dia- 
grams from the three cylinders 
and the two receiver spaces are 
combined, so as to show the true relations of volumes and 
pressures. 

Indicator-diagrams were taken with a Crosby indicator, and 
in order to get clear diagrams the main group of experiments 
were made at 400 revolutions per minute, but in practice it is 
the habit to run at 500 revolutions per minute. 

In comparing these tests it was assumed that the work 
theoretically due to the heat in the steam was the heat changed 
into work by an engine working on the cycle represented by 




366 



THERMODYNAMICS OF THE STEAM-ENGINE. 



was assumed that dry saturated steam was ad- 
absolute pressure /j from ato b\ that the steam 





Fig. 69. 

was expanded adiabatically from b 'lo c till the absolute pressure 
b^ame p^ ; and that the steam was exhausted 
i* against a constant pressure. 

The efificiency of this cycle may be cal- 
culated as follows : The work of M pounds 
of steam during admission is 

The work during expansion by equation (156), page ill, is 
M 

The work during exhaust is 



VARIOUS STEAM-ENGINE TESTS. 36/ 

The work done by the steam during the cycle is 
M 

M 
'''W = -j{r,-x,r,-]rq,-q^ (307) 

But by equation (146) 

■*■ \ J- 1 

which, introduced into equation (307), gives 

+ U(^.-^) + q.-q)^^ (308) 



A 



Mr. Willans used 770 for the mechanical equivalent of heat 
and 461° for the absolute temperature of the zero of the Fah- 
renheit scale, and gives as an approximation for equation (308) 

^^Z&.+^T^)^^--^^)' • • • (309) 



and for the steam used per horse-power per hour 

2571 



[t,'^ T.+ fJ^-^' '^^ 



(310) 



which may be compared with equation (243), page 180. 

The best ratio of expansion was determined, for any given 
absolute pressure, by aid of the diagram Fig. 71. The abscissae 
represent volumes, and the ordinates the work calculated by 
equation (309). Ob represents the volume of M pounds of 
steamx admitted at the absolute pressure of 50 pounds. \a 



368 



THERMODYNAMICS OF THE STEAM-ENGINE. 



represents the total work done during the admission, of which 
\b must be expended in overcoming the back pressure during 
exhaust, leaving the useful work ab. The lines 2c, 3^, etc., rep- 
resent the total forward work during admission and expansion 
to 2 times, 3 times, etc., the original volume, of which the 
portions 2d^ 3/, etc., represent the work of overcoming the 




Fig. 71. 

back pressure, and the portions cd, ef, etc., represent the useful 
work. The limit of useful expansion is that at which the use- 
ful work becomes a maximum. The line xy is drawn through 
the points on the curves for the several pressures, beyond which 
little or no gain is obtained from further expansion. The dia- 
gram is for a non-condensing engine exhausting against the 
pressure of the atmosphere, and it is apparent that much greater 
expansion would be advisable if the engine were condensing 
with a small absolute back pressure. 

The nominal ratio of expansion in each test was fixed by 
dividing the volume of steam at the terminal pressure, exhausted 
from the low-pressure cylinder, by the capacity of the high- 



VARIOUS STEAM-ENGINE TESTS. 



369 



pressure cylinder at cut-off, neglecting clearances. The volume 
exhausted was assumed to be represented by the line CB in 
Fig. y2. This line CB was assumed to be 0.95 of the stroke, 
represented by AB. 

During the tests the power of the engine was absorbed by 
a dynamo-machine, the load being adjusted by regulating the 
resistance in the circuit. 

The feed-water was drawn by the feed-pump from a tank 
holding sufficient water for a test and mounted on a weighing- 
machine. The weight of the tank and water was noted at the 





^>( 


^X^Point of Cut Off 




\l 

aVc___ 

1 V 


— H 


-1-^;^^:::=::: 





Fig. 72. 



beginning and end of the test, at which times the suction of 
the feed-pump was disconnected. Before beginning a test the 
water in the boiler was raised above the middle of the glass 
water-gauge, and the feed-pump was disconnected while the 
weight was taken. When the water in the glass gauge reached 
a standard mark at about half the height of the water-gauge, 
the time of beginning the test was noted, a counter was thrown 
into gear, the feed-pump was connected and started, indicator- 
diagrams were taken, and temperatures were read on ther- 
mometers. A few minutes before the conclusion of a test the 
water was raised in the boiler about half an inch above the 
reference-mark on the glass gauge, and the feed-pump was dis- 
connected and the weight of the tank and water was taken. 
When the water reached the reference-mark on the gauge the 
time was noted as the end of the test, and the counter was 



370 



THERMODYNAMICS OF THE STEAM-ENGINE. 



thrown out of gear. The only source of error was the uncer- 
tainty of the height of the water in the glass gauge, which gave 
an error not exceeding 0.25 per cent. 

The pressure in the boiler rarely varied two pounds in any 
test. Three sets of indicator-diagrams were taken each hour, 
which were practically identical. 

The largest cylinder, nearest the crank, is called the low- 
pressure or l.-p. cylinder ; the other two cylinders are called 
the high-pressure or h.-p. cylinder, and the h. h.-p. cylinder. 
The main dimensions of the engine are given in the following 
table : 



V/illans Engine, 




Stroke, 


6 in. 


Diameters : h. h.-p. cylinder, . 




. 7 " 


h.-p. cylinder, . . 




. 10 " 


l.-p. cylinder, . . 




. 14 " 


Net area : h. h.-p. piston, . . 




. 34.500 sq. in 


under side of same. 




. 31.416 - 


h.-p. piston, . . . 




. 71.472 " 


under side of same, 




. 65.973 " 


l.-p. piston, . . . 




. 141.340 " 


Capacity of trunk clearance : h. h.-p.. 


. I I.I cu. in. 


h.-p., . 


. 15.0 - 


i.-p.. . 


. 26.0 " 


Capacity of cylinder clearance : h. h.-p 


)., 14.8 '' 


h.-p., 


. 30.0 " 


1. 


-Pv 


. 33.6 " 

• »T« 1 1 -« 



The data and results of the tests are given in Tables XXV 
to XXXI. 

In Table XXV the ratio of expansion corrected is deter- 
mined by dividing the volume of steam at the terminal pres- 
sure, discharged from the l.-p. cylinder by such a volume of 
steam at mean admission pressure as would agree with the 
steam shown '^y the indicator at the point of cut-off. This 
method of calculating the expansions takes account of steam 



VARIOUS STEAM-ENGINE TESTS. 



371 



TABLE XXV. 
Tests on Willans Engine — Simple, Pressure Varied. 



Dec. 9... 
Dec. 6... 
Dec. 8... 
Nov. 30. 
Nov. 30. 
Dec. 7. . 
Dec. 5... 



270 
242 



176 
298 



e-r 



3 c 



.E >. 
o w 

04 



0.604 

0-437 

0-339 

0.296 

0.264 

0-2375 

0.216 



So 



14.49 
14.46 
14-57 
14.66 
1475 
14.64 
14.74 



Pressures. 



Is 

'o ^ 



36-25 
51.0 
74.0 
85.0 
97.0 



c 
c-r 

Vh ti U5 

cj 3 t/l 
C en O 

U 



40.88 
50.65 
68.67 
78.66 
92.65 
98.14 
106.34 



a 


•0 







c 




a 












rtJtt 


^^•> 




oV 


?i-S 


3 3 


3 i^ 


•° 


0^ 


°:: 


C M 


.0 


XI 


D rt 


< 


< 


^ 


10 


11 


12 


35-7 


22.1 


14-8 


42 


8 


20.2 


14.46 


5« 


2 


22.9 


15-4 


6,5 


4 


22.12 


15-4 


76 


3 


23.8 


15-6 


80 


2 


23.6 


15-4 


87 


I 


23.5 


15.0 



a 



o u a 



13 

19.6 

22.62 

29.14 

31.06 

36.83 

36.87 

38.61 





u 


Steam per indicated 





la 


Percentage of 
total feed-water 


Heat units 




s. 


horse-power per hour. 


.Si 
"0 
5E 


^a 


missing. 


missing. 


« 


v 








<-> a 








^ 


«2 


UJ 




rt 








a 






3 







3 




u 


!>. 




(U — 


'. 


d. 


a 




^"^ 
•^I'- 

s^-^ 


ll 


5i 


M 










5tt oj 


}ji 




rt . u 

3 '."a 
0— G 


t'i 


nJ 


C -i 


St: So 


?^ 


^ 1- (U 


3;^ 




c o;r; 


.G ,, "'^ 


m :^-^ 


•^ ° 






o- j; c 


ii 


(«• «Jx: 


>, 


oh >^ 


<u h >^ 


V^tt >, 


i_ 3 >» 


? 0. 


«x: 


>, 


>.<J 


aj au 


<u 




.^ 


4J en 


4J (« y 


w 


u u y 




tL, 


m 


pa 


C«J 


Dm 


J 


< 


< 


< 


Ph 


^ 


14 


15 


16 


17 


18 


19 


20 


21 


22 


23 


24 


25 


16.51 


706.0 


42 76 


37-74 


34-67 


81.08 


4.6 


II. 7 


II. 7 


10.4 


77-213 


3-269 


19.77 


711. 


35.96 


29.03 


28.62 


79.58 


6-5 


19-3 


20.53 


17-58 


126.588 




166 


25 51 


830.8 


32.57 


23.92 


23.02 


70.6 


2.7 


26.5 


28.02 


19.26 


200.544 


8 


168 


26.8 


795-2 


29 67 


22.62 


21.15 


71.6 




23-7 


24.1 


19.2 


170.494 


7 


048 


SI. 61 


850.0 


26.89 


20.21 


19.24 


71.5 


8.0 


24.8 


23-3 


18.83 


189. 140 


7 


863 


31.49 


877.7 


27.8 


19.7 


18.66 


67.1 


7-2 


31-25 


27.7 


23-44 


244.866 


10 


261 


33.55 


874.4 


26.0 


18.36 


17.9 


68.8 


2.8 


29.56 


26.7 


21-53 


229.976 


9 


436 



required to fill clearances, but not of steam condensed during 
admission. 

The cylinder pressure during admission, column 9, is the 
pressure from the indicator-diagrams, at a point midway be- 
tween the beginning of the stroke and the point of cut-off. 

The total mean pressure referred to the low-pressure cylin- 
der, column 13, is, in Table XXV, simply the mean effective 
pressure. In the triple and the compound tests it is that mean 
effective pressure which, acting on the large piston, would give 
the indicated horse-power of the engine. 



3/2 THERMODYNAMICS OF THE STEAM-ENGINE, 

In calculating the steam per horse-power per hour shown 
by the indicator, column 17, there are two clearance spaces to 
be considered. One is the passage in the trunk between the 
cut-off ports and the valve-ports, which is filled from the back 
pressure to the pressure during admission. The other is the 
true cylinder clearance, which is filled from the pressure at the 
end of compression to the pressure during admission. 

The steam per horse-power per hour, column 18, is calcu- 
lated for the mean admission pressure by equation (310). 

The percentage of efficiency, column 19, is obtained by 
dividing the steam per horse-power per hour required by a 
perfect engine by the steam actually used and weighed in the 
tank. Unless the method of determining this quantity is 
borne in mind the results in the tables are liable to be mislead- 
ing. 

The heat units missing at cut-off, column 24, are calculated 
on the assumption that all the steam not accounted for by the 
indicator at that point is present in the form of water at the 
temperature which the steam then has. 

The heat units missing per stroke, column 25, are inserted 
to facilitate the comparison between the missing heat and the 
changes of temperature and surface of the cylinder walls, which 
are usually supposed to account for it. 

The columns added in other tables are those required by 
the use of the steam in two or three cylinders. 

Discussion of Results. — The tests made with the large 
cylinder only, that is, the simple tests given in Table XXV, 
show a regular decrease in the steam actually used per horse- 
power per hour, as the steam pressure and the number of ex- 
pansions are increased simultaneously, with the revolutions 
nearly constant at 400 per minute. It is notable that the ratio 
of the steam shown by the indicator at cut-off to the steam 
used by a perfect engine is nearly constant, and but little larger 
than one. This, together with the increased condensation and 
re-evaporation, explains why the percentage of efficiency, so 
called, should diminish as the steam pressure and ratio of ex- 
pansion increase. 



VARIOUS STEAM-ENGINE TESTS. 



373 



TABLE XXVI. 

Tests on Willans Engine — Simple Speed Tests. 







- 


d. 




c 




Pressure. 












'.S '-" 


„• 


c 

■35 


So.^ 
















is 




e 




i 


<u 6 


a 

(U 3 


G 

a 


•a 

a 




d 


a 
"0 


1 

2 


.11 

4> n 


3 ^ 


t 

"Z! 


1^ 

6 




a 



II 


Ill 


rtStJ 
J? 

1^ 




^6 

11 


c *-• 


rt 


3 


<-> 


rt 


g V. 


n! 


rt 


>>a5 c« 




Si 




w 0- 


Q 


Q 


Oi 


P-. 


05 


H 


m 


m 


U 


<1 


<3 


^ 


H 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


[11 


12 


13 


Dec. 6... 


270 


408.4 


0.437 


2.43 


65 


14.46 


51.0 


50.65 


42.8 


20.2 


14.46 


22.62 


Dec. 7... 


153 


200.6 


0.437 


2.3 


60 


14.57 


44.0 


49.55 


43-6 


21.7 


15.2 


21.72 


Dec. 6... 


122 


no. 5 


0.437 


2.25 


50 


14.44 


40.25 


49.04 


43-8 


22.1 


14.7 


23.13 


Dec. 8... 


242 


409.1 


0.339 


3.09 


65 


14-57 


74.0 


68.67 


58.2 


22.9 


.15.4 


29.14 


Dec. 9.. 


152 


205.2 


0.339 


3.087 


66 


14.47 


66. S 


71.07 


60.1 


2=^.2 


15.1 


32.0 


Dec. 8... 


127 


112. 7 


0.339 


2.99 


68 


14.40 


62.0 


69.1 


60.6 


26.8 


14.65 


32.9 


Nov. 30.. 


180 


400.9 


0.264 


3.85 


.S8 


14.75 


97.0 


92.65 


76-3 


23-8 


15.6 


36.83 


Nov. 30.. 


118 


223.0 


0.264 


3-74 




14.7 


84.7 


88.46 


74.6 


23.1 


15.5 


35-1 


Dec. I... 


178 


122.8 


0.264 


3-72 


66 


14.93 


80.0 


89.43 


75.6 


27.0 


15-4 


38.0 


Dec. 5... 


2q8 


406.16 


0.216 


4-57 




14.74 


122.0 


106.34 


87.1 


23.5 


15.0 


38.61 


Dec. 2... 


119 


223.7 


0.216 


4.46 




14.98 


112. 


108.98 


90.0 


28.1 


15.5 


42.8 


Dec. 5... 


123 


138.0 


0.216 


4.32 




14.74 


105.4 


108.72 


93.1 


28.4 


15.5 


44-31 







Steam 


per indicated 





la 


Percentage of 
total feed-water 


Heat units 






horse-power p. hour, lbs. 


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711. 


35.96 


29.03 


28.62 


79.58 


6.5 


19-3 


20.53 


17.58 


126.588 


S.i66 


19.32 


389.4 


41.78 


31 79 


2915 


69.7 


8.0 


23.9 


24.5 


17.57 


85-931 


7.139 


6.47 


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30.16 


29-37 


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34.5 


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25.51 


830.8 


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26.5 


28.02 


19.26 


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8.168 


14.05 


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34.4 


22.55 


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22.08 


22.9 


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41.63 


32.71 


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19.864 


31.61 


850.0 


26.89 


20.21 


19.24 


71 5 


8.0 


24.8 


23-3 


18.83 


189.140 


7-863 


16.75 


465.25 


27.77 


20.8 


19.71 


70 9 




24.75 


23-4 


19.52 


101.216 


7-564 


9.98 


339-8 


34.05 


19.61 


19.64 


57.6 




42.5 


37 7 


28.70 


129.168 


17-523 


83.55 


874.4 


26 


18.36 


17.9 


68.8 


2.8 


29.56 


26.7 


21.53 


229.976 


9-436 


20.49 


618.6 


30 19 


17.41 


17.68 


57.66 


4.0 


42.33 


35.58 


26.26 


232.556 


14.338 


13.09 


408.8 


31.22 


17.41 


17.7 


56.6 


3-0 


44-5 


38.2 


30-65 


161.254 


19-475 



374 THERMODYNAMICS OF THE STEAM-ENGINE. 

Table XXVI gives four groups of three tests each, made 
on a simple engine with the steam pressure and ratio of expan^ 
sion nearly constant, and with the speed varying from about 
lOO to about 400 revolutions per minute. They indicate a 
regular and notable reduction of steam consumption per horse- 
power per hour, and a regular gain of efficiency, with a marked 
reduction of initial condensation. 

Four series of tests on the engine running compound were 
made ; those in Table XXVII were made with the speed con- 
stant and the number of expansions varied according to the 
method shown in Fig. 71 ; those in Table XXVIII were made 
with the pressure constant and the ratio of expansion varied ; 
those in Table XXIX were made in three groups, in each of 
which the number of expansions was constant and the pressure 
varied ; those in Table XXX were made in three groups of 
three each with a varying speed. 

In Table XXVII the tests stated in italic numerals were 
made with the ratio of expansion given by the expression 



25' 

and the others with the ratio of expansions determined by the 
expression 

/ — 10 

in which / is the absolute steam pressure. The effect of this 
variation of the number of expansions is shown by Fig. 73 ; on 
which are plotted also the consumption for a perfect engine of 
the type represented by equation (308), and the consumptions 
of the engine when working simple and when working com- 
pound. 

As with the simple tests, the consumption of steam per 
horse-power per hour decreases with the simultaneous increase 
of steam pressure and expansion ; but the percentage of effi- 
ciency does not show a notable falling off till the boiler-pres- 
sure reaches 130 pounds above the atmosphere. 



VARIOUS STEAM-ENGINE TESTS. 



375 








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VARIOUS STEAM-ENGINE TESTS. 



Z77 



The reduction of initial condensation by compounding is 
very noticeable, and is accompanied by a marked reduction of 
steam consumption at and above 80 pounds absolute. If we 
may assume that the curve for the compound engine with 

P 
the expansion — can be produced, it would show that com- 
pounding ceases to be of value somewhere between 50 and 60 








































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100 no 120 130 140 
steam Pressure, (absolute.) 



160 170 180 190 SQOlbS. 



Fig. 73. 



pounds absolute, provided that the engine exhausts against 
atmospheric pressure. 

Table XXVIII gives the results of tests made with a con- 
stant steam pressure and varying expansion, while Table XXIX 
gives the results of tests made with fixed rates of expansion 
and varying pressure. A comparison of these tables with Table 
XXVII shows that the rates of expansion in the latter are well 
chosen. 



378 



THERMODYNAMICS OF THE STEAM-ENGINE. 



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VARIOUS STEAM-ENGINE TESTS. 



3/9 



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THERMODYNAMICS OF THE STEAM-ENGINE, 



2 . 

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VARIOUS STEAM-ENGINE TESTS. 38 1 

Table XXX gives the results of tests made with speed vary- 
ing from 100 to 400 revolutions per minute. These tests, like 
the simple speed tests, show a reduction of steam consumption 
at higher speeds and a corresponding improvement in efficiency, 
due to the reduction of initial condensation. Mr. Willans points 
out the fact that the total initial condensation in a given time 
remains nearly constant for these compound speed tests, so 
that doubling the speed of rotation reduces the initial conden- 
sation per stroke one half. He also shows that this does not 
hold for the simple speed tests. 

Table XXXI gives the results of tests made with the en- 
gine running with triple expansion. A comparison with the 
results of Table XXVII shows that it is advisable to use a com- 
pound engine below 160 pounds pressure absolute, and a triple- 
expansion engine above 'that pressure. The curves of steam 
consumption in Fig. 73 indicate the same fact. In connection 
with this conclusion, and when considering the small degree of 
expansion used even with high-pressure steam, it is to be re- 
membered that this engine exhausted against the atmosphere. 
Were a condenser to be used with the engine, and a back pres- 
sure of two pounds absolute assumed, then the method used 
for determining the ratio of expansion would give results more 
nearly in accord with the ordinary practice with compound and 
triple-expansion engines, which commonly work under such con- 
ditions. 

To determine the leakage past valves and pistons the en- 
gine was blocked in various positions and exposed to the pres- 
sure of steam from the boiler ; meanwhile the water-level in 
the boiler was watched, and the fall of water was assumed to 
be due to leakage and condensation. The largest amount thus 
determined was 15 pounds per hour — too small a quantity to 
be satisfactorily determined in that manner. 

A separator was at first put on the steam-pipe for the pur- 
pose of abstracting the condensation in the steam-pipe and 
priming from the boiler, but the entire amount collected in an 
hour was three pounds, therefore the separator was removed. 

Afterwards calorimeter tests of the quality of the steam 



382 



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VARIOUS STEAM ENGINE TESTS. 



383 



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384 



THERMODYNAMICS OF THE STEAM-ENGINE, 



from the boiler were made by blowing a hundred-weight of 
steam into the water in the iron feed-tank arrd noting the rise 
of temperature. The results of the tests are given in the fol- 
lowing table, in which w is the weight of the water in the tank 
and the water equivalent of the iron forming the tank, u is the 
weight of the steam blown in, p is the absolute pressure of the 
steam, and t^ is the corresponding temperature, while t^ and t,^ 
are the initial and final temperatures of the waterin the tank; 
x' is the percentage of steam using Regnault's value of the 
total heat of steam and heat of the liquid ; x is the percentage 
of steam corrected for Bosscha's specific heat for water. 
Quality of Steam used in Willans Engine. 





















Duration 




No. 


^ 


t-i 


h 


h 


w 


u 


x^ 


X 


of blow in 
minutes. 


Remarks. 


I 


105 


8.505 


24.30 


160.0 


4416 


"0.375 


99.82 


99.96 


7.0 


) Steam blown into 
f warm water. 


2 


173 


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39-3 


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4181 


109.4 


96 


87 


96 


38 


7.0 


3 


160 


II. 6 


25.81 


184.0 


4919 


110.38 


99 


27 




488 


8.0 


Steam blown in 


4 


139 


12.00 


25.82 




4921 


no. 2 


9b 


29 


96 


40 


4.0 


f very fast. 


S 


154 


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29.4 


183 


5032 


109.97 


99 


66 


99 


76 


15.0 


6 


162 


9.10 


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185.0 


4947 


III. I 


98 


63 


98 


93 


4-5 


i Water in boiler 
f low. 


7 


178 


9.827 


23.501 


188.8 


5263 


112. 


100 


4 


100 


72 


12.0 


8 


65 


10.77 


25 19 


147.8 


4898 


112. 


100 


8 


100 


48 


9.0 




9 


127 


8.18 


22.73 


174.0 


483b 


no. 8 


99-63 


99-873 


9.0 





The diagram in Fig. 74 is given to show the increase of 




:fig. 74. 



the pressure in the steam-chest above the boiler-pressure after 
cut-off, due to the velocity and the density of the steam at 160 
pounds pressure. 



VARIOUS STEAM-ENGINE TESTS. 



385 



The diagrams in Figs. 75, y6, and JJ were taken from the 
compression chamber between the low-pressure cyHnder and 
the engine-shaft. Fig. 
^6 was taken under the 
normal condition with dry 
air in the compression- 
cylinder, in which case the 
compression and expan- 
sion curves are scarcely 
distinguishable, and are 
both sensibly adiabatic. 
Fig. 75 was taken when 
a considerable amount of 
water was purposely in- 
jected into the compres- 
sion-cylinder, and Fig. 77 
was taken with steam in 
the cylinder instead of 
air : both indicate an ener- 
getic interchange of heat 
between the fluid and the 
cylinder walls. 

Institute of Technol- 
ogy Tests. — The tests 
recorded in Table XXXII 
are one series of a large 
number of tests on simple o 
engines, made in the me- 




FiG. 75. 



Fig. 76. 



chanical engineering laboratory of the Massachusetts Institute 




o 



Fig. 



of Technology, and forming a part of the regular instruction 
in that laboratory. 



386 



THERMODYNAMICS OF THE STEAM-ENGINE. 



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VARIOUS STEAM-ENGINE TESTS. 38/ 

The engine on which the tests were made is the Harris- 
Corhss engine, referred to on page 333, having a stroke of 24 
inches and a diameter of 8 inches. The cyhnder is covered 
with hair felt and wood lagging, but is not steam-jacketed. It 
is supplied with steam containing from one to two per cent of 
moisture, as determined by a large number of tests with sev- 
eral kinds of calorimeters. 

During the tests the steam used was condensed in a surface 
condenser, collected and weighed. Indicator-cards were taken 
at intervals of five minutes simultaneously, from each end of 
the cyhnder, and at the same time the necessary temperatures 
and pressures were read and recorded, and the revolutions were 
read on a counter. The data in the tables are determined from 
the totals or averages of the observations taken during the test. 

The errors of all the instruments used during the tests were 
determined in the laboratory, and corrections were applied when 
necessary. 

To insure regularity of results in this series the following 
precautions were taken: (i) the governor of the engine was 
disconnected, the cut-off mechanism was fixed by hand, and 
the engine was coupled to another engine to control the speed ; 
(2) the steam-pressure was maintained as nearly constant as 
possible during a single test ; (3) the tests of the series all have 
nearly the same boiler-pressure ; (4) during the tests the throt- 
tle-valve was wide open. A comparison of the tests of this 
series with other tests on this engine, in which some of the 
conditions could not be fulfilled, shows clearly that all are requi- 
site if definite results are to be attained. 

Tests of a Worthington High-duty Engine. — In Table 
XXXIII are given the data and results of two tests made by 
Prof. Unwin * on a Worthington high-duty duplex compound, 
pumping engine, with compensating cylinders, built by Messrs., 
Simpson & Co., Pimlico, and operating at the West Middlesex 
Water-works at Hampton. 

The engines of this type have no fly-wheel nor heavy recip- 
rocating mass, but provision is made for cut-off and expansive 
working of steam in the high-pressure cylinder, by aid of a pair 

* Engineering, Dec. 1888. 



388 THERMODYNAMICS OF THE STEAM-ENGINE. 

of compensating cylinders for each piston-rod. The piston-rod 
carries the two steam-pistons at one end, the pump-plungers 
at the other end, and near the pumps is operated on by the 
compensating cylinders, which are swung on trunnions in 
such a manner that they oppose the motion of the piston-rod 
at a considerable angle at the beginning of the stroke, offer a 
less resistance as the stroke proceeds, till at half-stroke they are 
opposed to each other and mutually counterbalance each other ; 
and during the second half of the stroke, when the steam pres- 
sure in the cylinder is reduced by expansion, they restore the 
work stored during the first half, and help the pump to com- 
plete its stroke. 

The engines tested are used to pump a large volume of 
water on a comparatively low lift. The high-pressure pistons 
are 27 inches in diameter, and the low-pressure pistons are 54 
inches in diameter. The maximum stroke is 44 inches; during 
the test the stroke remained very constant at 43 inches. The 
main valves of each engine are worked by the other engine, 
but the independent cut-off valves of each engine are worked 
from its own piston-rod, and there is an independent control 
of the compression in the high-pressure cylinder. The engines 
work directly double-acting ram-pumps, the rams being 40 
inches in diameter, and having the same stroke as the steam- 
pistons. The valves are of India rubber, spring loaded, and the 
slip is probably small. The compensating pistons are 1 1 inches 
in diameter, and are loaded with an air-pressure of 120 pounds 
per square inch. The pumps lift water from a well communi- 
cating with the river and deliver it through two 3-feet mains to 
reservoirs nine miles distant. The head during the tests, meas- 
ured by the difference of pressure in the suction- and discharge- 
pipes, was from 50 ft. to 65 ft., which head was almost entirely 
expended in overcoming the friction in the mains. 

The engine cylinders are completely jacketed, and the steam 
is also taken through a jacketed reservoir between the cylinders. 
The jacket-water was discharged through a pipe regulated by 
a stop-valve and weighed. The condensers are injection-con- 
densers with horizontal air-pumps. 



VARIOUS STEAM-ENGINE TESTS. 389 

The boilers are single-flue Cornish boilers. Three were 
used during the trial on October 29th, and four during the trial 
on November 5th and 6th. The boilers are 28 ft. long and 
6 ft. in diameter, with a flue 3 ft. 6 in. in diameter. During 
the trials on November 5th and 6th the length of the grate was 
4 ft. 6 in., making an area of 60 sq. ft. 

The coal was weighed on platform scales which had been 
tested. 

The feed-water was supplied from the delivery main at a 
temperature of 51 degrees. The ordinary feed arrangements 
for supplying hot water from the jackets and hot-well were dis- 
connected. The feed-water was measured in a gauge-tank, of. 
which the capacity was obtained by weighing in water at the 
temperature used during the tests, so that no corrections for 
temperature were required. 

The feed-tank delivered by a stop-valve into another tank, 
from which a small Worthington feed-pump delivered the water 
into the boilers. 

The Worthington pump took its steam from the boilers in 
use and exhausted into the tank, from which it pumped. The 
whole of the steam used was therefore recondensed and returned 
to the boilers. 

Of the heat supplied by the boilers to work the feed-pump 
nearly all was returned to the boilers. A small portion, viz.. 
that due to the useful work of pumping and that lost by radia- 
tion from the tank, was no doubt lost. So far, a small error 
telling against the main engines is introduced. 

The water-level at the commencement of each trial in the 
boiler gauge-glasses was carefully observed, and the water-level 
was brought to exactly the same marks at the end of the trials. 
Hence no correction has to be made for difference of level in 
the boilers. The time at which each tankful was supplied to 
the boilers was noted, and also the feed-water temperature. 
Pyrometer observations were made in the flues with two Hur- 
ries pyrometers. During part of the trial one of these had to 
be used at temperatures near the bottom of its scale, where the 
indications are least trustworthy. But the mean of the py- 



390 THERMODYNAMICS OF THE STEAM-ENGINE, 

rometer readings is probably not very incorrect. Anemometer 
observations of the air supplied to each boiler were taken every 
half-hour during the twenty-four hours' trial, the anemometer 
having been previously tested. 

The air-pump discharge was led into a wooden tank with 
stilling screens. From this it was discharged through a sharp- 
edged circular orifice freely into the air. The diameter of the 
orifice was carefully tested after the trials, and the coefficient 
of discharge from similar orifices is known to be 0.599. The 
temperature and head over the orifice was noted every 5 min- 
utes in the first trial, and every 7^ minutes in the second. The 
temperatures relied on in this report were taken by a fixed 
zero thermometer, with open scale, recently verified at Kew. 

As the stroke is variable, an arrangement of indicating fin- 
gers was attached to each engine, and the length of stroke on 
each engine was noted every quarter of an hour. 

The indicated power was taken by four Richards indicators, 
chosen because they give fairly large diagrams. These indi- 
cators were sent to Kensington after the trials and tested under 
steam. No important error was found at any part of the scale 
with any of the springs. But with the light springs of the low- 
pressure cylinder indicators there was a little frictional sticking, 
or else a little slackness of the parallel motion joints, which 
under a steady pressure introduced a small uncertainty of in- 
dication at one or two points in the range. Probably this 
would be less still when the indicator-piston was in motion as 
when drawing a diagram. The indicator-pipes were large, and 
were clothed. Diagrams were taken every half-hour from all 
the cylinders, so that there were 128 single diagrams in the 
eight hours' trial and 384 in the twenty-four hours' trial. All 
the eight hours' trial diagrams were reduced by planimeter ; 
also all the diagrams taken in the first eight hours of the twenty- 
four hours' trial, and half of these taken subsequently. The 
conditions were so constant throughout the trial, and the dia- 
grams so similar, that this was thought sufficient. 

The trial of eight hours' duration on October 29th was of 
the engine only, and no account was taken of the coal burned. 



VARIOUS STEAM-ENGINE TESTS. 39 1 

During the trial on the 5th and 6th of November the coal con- 
sumption was measured as well as the efficiency of the engines. 
The engines, as before, had been started in the morning, but 
before beginning the fires were cleaned and all ashes removed ; 
also all coal was swept from the boiler-house floor. Four boilers 
were used, and the fires were not drawn ; but the condition of the 
fires was nearly identical at the beginning and at the end of the 
experiment. The fires were cleaned again about eighteen hours 
after starting, all the clinker and ash removed being placed in 
the ash-pits. At the end of the trial the fires were judged to be 
on the average slightly thicker than at the beginning of the 
trial. The trial commenced at 10.22 A.M. on the 5th and ended 
exactly at 10.22 A.M. on the 6th. The stoke-hole floor having 
been swept clean at the beginning of the trial, the coal was 
brought in in quantities of about 8 cwt., and the time of finish- 
ing each lot was noted. The ash-pits were cleaned before the 
trial, and afterwards nothing was removed till the end of the 
trial. The fires were cleaned before the trial began, and again 
at 4 A.M. on Tuesday morning. The fires were not touched 
at the end of the trial, but the ash-pits were immediately cleaned, 
and the whole of the ashes were treated thus : 

First the clinkers, including those removed from the fires at 
4 A.M. (six hours before the end of the trial), were separated 
and weighed. The rest of the ashes were sifted through a sieve 
with -J-in. mesh. All that passed through the sieve is treated 
as incombustible ash, although probably one third of it is un- 
burned carbon. What did not pass through the sieve is treated 
as unburned fuel. Analysis in similar cases has shown that the 
cinders retained by the sieve are almost entirely carbon. 



392 



THERMODYNAMICS OF THE STEAM-ENGINE. 



TABLE XXXIII. 
Diameter and Areas of Cylinders and Pumps. 





vS 


fe 


c 




rt 






rtfe 







"B 








^•s 


n 


S. 


^ 


% 


Mean. 




B be 


1? 




i 

< 




< 








in. 


in. 


sq. in. 


sq. in. 


sq. in. 




H. P. cylinder A: Back.... 


26.98 


27.02 


573-4 


17-7 


555-7 




front.. . . 


26.98 


27.02 


573-4 


23.8 


549-6 


' 553.5 


H. P. cylinder B: back 


27.02 


27.06 


575-1 


17.7 


557-4 


front 


27.02 


27.06 


575-1 


23.8 


551-3 




L. P. cylinder A: back 


53-99 


54-07 


2296.2 


7.0 


2289.2 




front 


53.99 


5407 


2296.2 


17-7 


2278.5 


V 2285. I 


L. P. cylinder B: back 


54 -02 


54.10 


2298.7 


7.0 


2291.7 


front 


54 -02 


54.10 


2298.7 


17.7 


2281.0 




Pump-plungers: back 


39-90 




1250.0 


16. s 


1233.2 


1241.6 


front 


39-90 


.... 


1250.0 





1250.0 



Tests of Engines. 



Date, . . 

Duration, 
Barometer, 



Vacuum, 



Head pumped against, . . . 

Total double strokes, . . . 

Length of stroke, minimum, . 

maximum, . 

Engine A: mean, 

B: " 

Delivery of pumps, not allowing 

for slip. 
Efficiency of machine, . 
Total feed-water, . . . 
" jacket- water, . . 
Double strokes per minute 
Boiler-pressure, . . . 
Feed-water per minute, . 
Jacket-drains per minute. 
Temperature of steam, . 
Pressure on pump, . . 

" in compensators, 
Mean pressure in H. P. cylinders 
L.P. 



Oct. 29th, 


Nov. 5th and 6th. 


8 hours. 


24 hours. 


30.166 


29.78 in. 


14.82 


14.627 lbs. per sq. in. 


28.04 


27.76 in. 


13.77 


13.63 lbs. per sq. in. 


60.63 


53-68 ft. 


8480 


24886 


4T.96 


42.32 in. 


43-56 


43-56 '' 


42.83 


43- 06 " 


43-00 


4305 " 


13-598 


13.407 gallons per min 


19580000 


19305504 gallons in 24h 


0.8434 


0.8495 


41277.8 


108537 lbs. 


5357 


<( 


17.67 


17.282 


75.2 


60.29 lbs. per sq. in. 


85.99 


75.37 lbs. 


II. 16 


11.77 " 


320.06 


307.36 degrees F. 


26.27 


23.26 lbs. per sq. in. 


120.6 


120 " " " 


39-23 


32.92 


7-42 


6.905 " " " 



VARIOUS STEAM-ENGINE TESTS. 393 

Temperature of injection, ... 54 49.2 degrees 
Temperature of air-pump dis- 
charge, 81.18 74 965 degrees 

Head over orifice, 1.9662 1.7033 ft. 

Air-pump discharge per minute, . 2777.7 2586 lbs. 

Injection-water, 2702,9 2522.4 lbs. 



INDICATED HORSE-POWER. 



Engine A: H. P. back, .... 37.78 31.662 

L. P. '• .... 34.19 71. 97l 31.14562.807' 

H. P. front, . . . . 3"^^^^ h^^-^ST^ U2^.(^(>% 



)-I28.( 



L. p. " .... 32.39 71.37J 31.685 65,86iJ 

Engine B: H. P. back, . . . . 45.68 35-856 

L. P. " .... 32.13 77. 8n 28.07363.929^ 

H. P. front, . . . . 43.93 M^'-^' 3!^ I126.849 

L. P. " .... 31.17 75.ioJ 27.684 62.920J 

Total indicated horse-power, both engines, 296.25 255.517 

Lbs. 

Total feed per indicated horse-power per hour, 17.41 17.700 

Jacket- water ditto, 2.26 2.763 

Used in cylinders, 15.15 14-937 

Heat absorbed by injection-water per minute, . 73,460 64,990 

Heat retained by condensed steam per minute, 1,958 1,519 

Heat retained by jacket-water per minute, . . 2,958 3,020 

Total, 78,376 69,529 

Heat rejected per indicated horse-power per 

minute, 264,6 272.1 

Add converted into work, 42.7 42.7 

Total, , 307.3 314.8 

HEAT PASSING THROUGH ENGINE PER MINUTE PER INDICATED HORSE-POWER. 

Thermal units from boiler in saturated steam 

through cylinders from feed temperature, . 292.0 287.8 

Latent heat of jacket steam, 33.6 41.45 

325.6 329-25 

Heat rejected in air-pump discharge, .... 254.6 260.24 

Converted into work, 42.7 42.75 

Radiation and error, 28.3 26.26 

325.6 329.25 

Indicated horse-power, 296.25 255.517 

Pump horse-power, 249.84 217.06 

Mechanical eflSciency, 8434 .8495 



394 THERMODYNAMICS OF THE STEAM-ENGINE, 

Feed per indicated horse - power per hour 

through cylinders, I5-I5 14-937 lbs. 

Feed per indicated horse - power per hour 

thi'ough jackets, 2.26 2.763 

Piston speed per minute 126.4 124 ft. 

Test of Boilers. 

Lbs. Lbs. 

Gross weight of coal brought into boiler-house, . . . it, 180 

Left on floor at end of trial, 99 

Cinders sifted out of ashes, 132 231 

Total coal used, 10,949 

= 456.2 lbs. per hour. 
Lbs. 
The residue consisted of clinkers, .,,,.,.. 66 

Incombustible ashes, 366 

432 

Percentage of clinkers and ashes, 3.9 lbs. 

Coal per sq. ft. of grate per hour, 7,24 lbs. 

" " " " heating surface per hour, 0.19 " 

Coal per indicated horse-power per hour, 1-785 " 

Water evaporated per pound of coal from 51°. 07 and at 307°. 36, 9.914 " 

" " " " " " " and at 212°, . . . 11.867 lbs. 

Estimated heat of com.bustion of coal, allowing for i per cent 

of moisture, 14878 B. T. U. 

Thermal units per horse-power per minute, estimated from coal 

consumption, 442.6 B. T. U. 

Thermal units per horse-power per minute, estimated from 

boiler steam (including loss by radiation), 34I-I " 

Efficiency of boiler, 0.77 

Cubic feet of air per minute by anemometer, 1704 

" " " " " pound of coal 225 

Pounds of air per pound of coal, 16.42 

Thermal Units 
per Indicated Per 

-._ , , , . , ., Horse-power cent. 

Heat used and lost m boilers: per Hour. 

Total heat due to coal used, ..,.,.,. 26,557 100 

Given to steam 20,466 77.1 

Carried off in furnace gases, 2,657 10. o 

Probable loss due to opening fire-doors to stoke, . 265 i.o 

Due to carbon in ashes, 284 i.i 

Radiation and unaccounted for, 2,885 10.8 

Duty of engine per 112 lbs. of coal: 24 hours' trial, actual, 106,000,000 ft. -lbs. 

8 " " estimated, 106,500,000 " 

Corrected for difference of temperature of feed-water from 

hydrant and from hot-well, 111,500,000 " 



CHAPTER XIX. 

FRICTION OF ENGINES. 

As has been stated in the discussion of the efficiency of the 
steam-engine, the economic value of an engine is determined 
by the net or brake horse-power, which is the indicated horse- 
power less the power used up by the friction of the mechanism 
of the engine. 

Pambour's Method. — It was suggested by Pambour that 
the friction of the engine could be divided into two parts, one 
of which remains constant and can be determined by indicating 
the engine without a load, and the other of which increases 
with the load and is proportional to it. In form of an equa- 
tion this becomes 

F = P„^fP, ...... (311) 

in which F is the horse-power lost in friction in the engine, P^ 
is the power required to run the engine unloaded, and P is the 
useful or net horse-power, while / is the coefficient for the in- 
crease of friction with the load. The work expended on the 
air-pump is counted with the friction for condensing engines. 
The efficiency of the mechanism is 

p p R-F 



F-\-P Pi Pi ' 

Pi being the indicated horse-power. 

Rankine "^ states that the unloaded resistance P^ is equiva- 
lent to a pressure of \ to \\ pounds to the square inch of the 
piston ; this may be compared with Isherwood's results on 
pages 265 and 274. He further states that the value of / = ^, 

* Steam-engine and Other Prime Movers, p. 423. 

395 



39^ THERMODYNAMICS OF THE STEAM-ENGINE. 

proposed by Pambour, is corroborated by general experi- 
ence. 

Alsatian Experiments.— In Tables XXXIV, XXXV, and 
XXXVI are given the results of tests made by Walther-Meu- 
nier and Ludwig,* to determine the friction of a horizontal 
receiver compound engine, with cranks at right angles and with 
a fly-wheel, grooved for rope-driving, between the cranks. The 
piston-rod of each piston extended through the cylinder cover 
and was carried by a cross-head on guides, and the air-pump was 
worked from the high-pressure piston-rod. The cylinders each 
had four plain slide-valves, two for admission and two for ex- 
haust ; the exhaust-valves had a fixed motion, but the admis- 
sion-valves were moved by a cam so that the cut-off was deter- 
mined by the governor. 

The main dimensions of the engine were : 

Stroke, . . i.i metres. 

Diam,eter: small piston, 0.536 

large piston, 0.800 

piston-rods, O.080 

Length of connecting-rods, .... 2.475 

Diameter, air-pump pistons, .... 0.360 

Stroke, air-pump, 0.476 

Diameter, fly-wheel, 6.610 

The engine during the experiments made 58 revolutions 
per minute. The air-pump had two single-acting vertical pis- 
tons. 

Each experiment lasted 10 or 20 minutes, during which the 
load on the brake was maintained constant, and indicator-dia- 
grams were taken. The experiments with small load on the 
brake— i.e.. No. 9, Table XXXIV ; No. 9 and No. 10, Table 
XXXV ; No. 9 and No. 10, Table XXXVI— were difficult and 
uncertain. 

The tests in Table XXXIV were made with the engine 
working compound. Those in Table XXXV were made with 
the high-pressure cylinder only in action and with condensation^ 

* Bulletin de la Soc. Ind. de Mulhouse, vol. Ivii. p. 140. 



FRICTION OF ENGINES. 



397 



the low-pressure connecting-rod being disconnected. Those 
in Table XXXVI were made with the high-pressure cylinder in 
action, without condensation. 



TABLE XXXIV. 



Tests. 


Horse-power— Chevaux aux vapeur. 


Efficiency. 








Nos. 


Effective. 


Indicated. 


Absorbed by. the 
engine. 




I 


248.97 


288.45 


39-48 


0.863 


2 


23S.92 


276.88 


37- 


96 


0.862 


3 


228.87 


265.62 


36 


75 


0.861 


4 


208 . 78 


243-72 


34- 


94 


0.856 


5 


18S.68 


222.73 


34 


05 


0.847 


6 


168.58 


201.48 


32 


90 


0.836 


7 


148.43 


180.44 


32 


04 


0.822 


8 


12S.38 


158.12 


29 


74 


o.8ii 


9 


108.28 


136.07 


27 


79 


0.795 


TABLE XXXV. 


Tests. 


Horse-power— Chevaux aux vapeur. 


Efficiency. 










Nos. 


Effective. 


Indicated. 


Absorbed by the 
eng-ine. 




I 


128.38 


153-12 


24-74 


0.839 


2 


118.33 


142.— 


23.67 


0-833 


3 


108.28 


130.89 


22.60 


0.827 


4 


98.24 


120.06 


21.82 


0.818 


5 


88.19 


108.96 


20.77 


0.809 


6 


78.14 


-97-45 


19-31 


0.801 


7 


68.09 


86.32 


18.23 


0.788 


8 


58.04 


75-72 


17.68 


0.766 


9 


47-99 


65.46 


17.47 


0.733 


lO 


37.94 


55-19 


17-25 


0.687 


TABLE XXXVL 


Tests. 


Horse-power— Chevaux aux vapeur. 


Efficiency. 


Nos. 


Effective. 


Indicated. 


Absorbed by the 












I 


128.38 


145-87 


17.49 


0.880 


2 


118.33 


135-73 


17 


40 


0.871 • 


3 


108.28 


125.17 


16 


89 


0.865 


4 


98.24 


T14.44 


16 


20 


0.858 


5 


88.19 


103.93 


15 


74 


0.848 


6 


78.14 


92.98 


14 


84 


0.840 


7 


68.09 


81.97 


13 


.88 


0.830 


8 


58.04 


71.72 


13 


.68 


0.809 


9 


47-99 


61.55 


13 


.56 


0.779 


lO 


37.94 


51-34 


13.40 


0.738 



398 



THERMODYNAMICS OF THE STEAM-ENGINE. 



The results of all of the tests are plotted in Fig. 78 with 
the effective horse-power for abscissae, and with the friction 
horse-power for ordinates. The lines may be taken to rep- 
resent the several series of tests, and the points where they 
cross the vertical axis may be considered to give P^ , the indi- 
cated power without a load, which was not determined directly. 




ABSCISSAE, EFHECTIVE HORSEPOWER. 
ORDINATES, FRICTION HORSEPOWER. 



250 



Fig. 78. 

Equation (311) for these several series of experiments be- 
comes : 

Compound condensing, 

/^ = 20 + 0.077P ; 
Small cylinder condensing, 

F — i\ +0.107P; 
Small cylinder non-condensing, 

F—(^-\- 0.062P. 

When the engine ran with the small cylinder only and with 
condensation, 27.74 horse-power were consumed by friction and 



FRICTION OF ENGINES. 399 

other resistances. Without condensation, and with the air- 
pump disconnected, 17.49 horse-power were thus consumed. 
The experimenters therefore considered that 7.25 horse-power 
Avere required to run the air-pump. From the mean vacuum 
they estimated the power required for the air-pump to be 7.38 
horse-power. 

The best efificiency in each case is found with the largest 
power. The tables give : 

Efficiency. 

Compound condensing, 0.863 

Small, cylinder condensing, 0.839 

Small, cylinder non-condensing, 0.880 

If the power required for the air-pump be deducted from the 
power absorbed by the engine, then the power used up by the 
friction of the mechanism divided by the indicated horse-power 
becomes, for the several cases : 

Compound condensing, 0.I13 

Small cylinder, condensing, 0.115 

Small cylinder, non-condensing, 0.12 

In the following table are given the results of other tests on 
engines of various types : 

TABLE XXXVII. 

Friction Tests of Engines. 



Date, 



1864- 
1867 
1876- 

1878 

1879 

1884 

1884 
1885 



Type of Engine, 



Single cylinder, beam with four 
valves, using superheated steam. 

Woolf , beam 

Horizontal Woolf small cylinder 
inclined 

Corliss 

Semi-fixed compound, horizontal 

Colman, horizontal < 

Horizontal portable 

Compound horizontal 



Names of Experimenters. 



Leloutre 

Grosseteste, Hallauer 

j Association Alsacienne; Wal- 1 

j ther-Meunier, Keller j 

j Association Alsacienne; Wal- 1 

I ther-Meunier, Keller (" 

J Association Alsacienne; Wal- i 

I ther-Meunier, Keller, ( 

i Association Alsacienne; Wal 
X ther-Meunier, Ludwig, A 

( Burghardt 

Association Alsacienne, Ludwig. 
J Association Alsacienne; Wal 
I ther-Meunier, Ludwig 



S2u > 

hH 1 



115 

191.44 
170.46 

144.82 

60. 

22.26 

23-97 
59-26 






908 
896 
891 

915 
876 

878 
863 



400 



THERMODYNAMICS OF THE STEAM-ENGINE. 



Thurston's Experiments. — As a result of a large number 
of tests on non-condensing engines, made under his direction 
or with his advice, Prof. R. H. Thurston^ concludes that, for 
engines of that type, the friction is independent of the load, 
and that it can, in practice, be determined by indicating the 
engine without a load. 

TABLE XXXVIII. 

Friction of Non-condensing Engine. 

Straight- line Engine, 8" X 14". 



No. of 


Boiler- 


Revolutions, 


Brake H. P. 


I. H. P. 


Frictional H. P. 


Card. 


pressure. 










I 


50 


332 


4.06 


7.41 


3.35 


2 


65 


229 


4.98 


7.58 


2.60 


3 


63 


230 


6.00 


10.00 


4.00 


4 


69 


230 


7.00 


10.27 


3-27 


5 


73 


230 


8.10 


11-75 


3.65 


6 


77 


230 


9.00 


12.70 


3.70 


7 


75 


230 


10.00 


14.02 


4.02 


8 


80 


230 


11.00 


14-78 


3.78 


9 


80 


230 


12.00 


15-17 


3-17 


10 


85 


230 


13.00 


15.96 


2.96 


II 


75 


230 


14.00 


16.86 


2.86 


12 


70 


230 


15.00 


17.80 


2.80 


13 


72 


231 


20.10 


22.07 


1.97 


14 


75 


230 


25.00 


28.31 


3-31 


15 


60 


229 


29-55 


33-04 


3-40 


16 


58 


229 


34-86 


37 -20 


2.34 


, 17 


70 


229 


39-85 


43-04 


3.19 


18 


85 


230 


45- 00 


47-79 


2.78 


19 


90 


230 


50.00 


52.60- 


2.60 


20 


85 


230 


55-00 


57-54 


2.54 



Table XXXVIII gives the details of one series of tests. 
The friction horse-power is small in all the tests, and the varia- 
tions are small and irregular, and appear to depend on the 
state of lubrication and other minor causes rather than on the 
change of load. Much the same result is shown by the tests 
given in Tables XXXIX and XL, the first on an automatic 
cut-off engine, and the second on a tandem compound engine. 

Distribution of Friction. — As a consequence of his conclu- 
sion in the preceding section, Professor Thurston states that 



* Trans, of the Am. Soc. of Mech. Engr., vols, viii., ix., and x. 



FRICTION OF ENGINES, 



401 



TABLE XXXIX. 

Friction with Change of Load. 

Automatic Engine, 12" X 18". 

Lansing Iron Works. Steam-pressure, 180 pounds. 



No. of 
Card. 


Revolutions 










per 
minute. 


Total I. H. P. 


Brake Load. 


Brake H. P. 


FrictionalH.P. 


I 


190 


11.20 


0. 


0. 


11.20 


2 


190 


II. 19 


0. 


0. 


II. 19 


3 


190 


10.80 


0. 


0. 


10.80 


4 


180 


8.27 


0. 


0, 


9.27 


5 


180 


8.76 


0. 


0. 


8.76 


6 


182 


13.24 


II-5 


2-79 


10.45 


7 


182 


13.55 


II. 5 


2.79 


10.76 


8 


187 


14.60 


21-5 


5-35 


8.25 


9 


187 


16.84 


22.5 


5.61 


11.23 


10 


1 80 


18.89 


23-5 


7-89 


11.00 


II 


192 


19-43 


46.0 


11.78 


7.65 


12 


192 


20.73 


49-0 


12.54 


8.24 


13 


192 


21.25 


49.0 


12.54 


8.71 


14 


192 


21.82 


49.0 


12.54 


9.28 


15 


190 


25-05 


72.5 


18.37 


6.68 


16 


192 


25-65 


72.5 


18.56 


7.09 


17 


192 


27-53 


77-5 


19.84 


7.69 


18 


185 


36.38 


115-5 


28.49 


7.89 


19 


185 


36.94 


120.5 


29.72 


7.22 


20 


180 


41.27 


142.0 


34-08 


7.19 


21 


180 


41.61 


142.0 


34.08 


7-53 


22 


180 


44.91 


150.5 


36.12 


8.79 


23 


175 


57-44 


210.5 


49-11 


8.33 


24 


175 


58 . 70 


209.5 


48.89 


9.81 



the friction of an engine may be found by driving it from 
some external source of power, with the engine in substantially 
the same condition as when running as usual, but without 
steam in its cylinder, and by measuring the power required to 
drive it by aid of a transmission dynamometer. Extending 
the principle, the distribution of friction among the several 
members of the engine may be found by disconnecting the 
several members, one after another, and measuring the power 
required to run the remaining members. 

The summary of a number of tests of this sort, made by 
Prof. R. C. Carpenter and Mr. G. B. Preston, are given in 
Table XLI. Preliminary tests under normal conditions .showed 



402 



THERMODYNAMICS OF THE STEAM-ENGINE. 



TABLE XL. 

Friction with Change of Load. 

Tandem Compound Engine, 14" and 21" by 20' 



No. of 
Card. 


Revolutions. 


I. H. P. for 
both cylinders. 


Brake Load. 


Brake H. P. 


Frictional H. P. 


I 


165 


55.86 


123 


27.12 


28.74 


2 


168 


57-55 


131 


29.26 


28.29 


1 3 


138 


79-97 


284 


52-15 


27.82 


4 


152 


84.16 


290 


58.81 


25 35 


5 


168 


73-65 


202 


45-25 


28.40 


6 


160 


82.08 


257 


54-83 


27.25 


7 


165 


81.36 


252 


55.44 


25.92 


8 


165 


82.26 


244 


53-67 


28.69 


9 


159 


85-44 


289 


61.27 


24.17 


10 


159 


86.04 


292 


61.90 


24.14 


II 


183 


51-11 


83 


20.26 


30.85 


12 


174 


68.45 


145 


33-75 


34-70 


13 


160 


86.77 


263 


56.11 


30.66 


14 


162 


80.65 


256 


55-28 


25.37 


15 


158 


82.31 


261 


55- 00 


27.31 


16 


160 


88.86 


298 


63-57 


25.29 


17 


156 


87.47 


283 


58.85 


28. 62 


18 - 


136 


86.35 


333 


60.38 


25.97 


19 


130 


83.03 


353 


61.19 


21.84 


20 


156 


29.22 


0. 


0. 


29.22 


21 


150 











22 


156 


27.63 


0. 


0. 


27.63 


23 


158 


29.69 


0. 


0. 


29.69 


24 


190 


127.10 


^ 







that the friction of the several engines was practically the same 
at all loads and speeds. 

The most remarkable feature in this table is the friction of 
the main bearings, which in all cases is large, both relatively 
and absolutely. The coefficient of friction for the main bear- 
ings, calculated by the formula 



/ = 



33000 H. P. 
pen 



is given in Table XLII. / is the pressure on the bearings in 
pounds for the engines light, and plus the mean pressure on 
the piston for the engines loaded ; c is the circumference of the 
bearings in feet ; n is the number of revolutions per minute ; 
and H. P. is the horse-power required to overcome the friction 
of the bearings. 



FRICTION OF ENGINES, 



403 



TABLE XLI. 
Distribution of Friction. 





Percentages of Total Friction. 


Parts of Engine. 


X > 

11 

v5« 


5i 

1 


'sis 
C^8 


i CO 


C ctf 




47.0 


35.4 


35.0 


41.6 


46.0 




Piston and Rod • 


32.9 


25.0 


21.0 


49.1 








Crank Pin 


6.8 
5-4 


5-1 
4.1 


13.0 


21.8 


Cross Head and Wrist Pin. . 


Valve and Rod 


2.5 

5-3 


26.4 
4.0 


22.0 


9-3 




Eccentric Strap 


21.0 






Link and Eccentric 






9.0 




12.0 






Total 


100. 


lOO.O 


100. 


lOO.O 


100. 







TABLE XLIL 
Coefficient of Friction for the Main Bearings of Steam-engines. 











c 


.2 

a 

c 


c 




6^ 


1 

<U 


























Engine. 




^ 

is 


3 Cfl 

J3 a 

tUD'"" 


en 


Wtd 

5E . 


c 
SEW 


Ml 3 

sis 

•a 










ffi 


'^ 


rt 


S5 


•oc 


£S 










fe 


^ 


Q 


U-s 


U 


Pi 


6' 


X 12' 

X 18' 






0.85 
3-70 


1500 
2600 


3 

5 




06 


230 
190 


*I2' 


Automatic (L. I 


.W.).. 


.19 


•05 


7' 


X 10' 


Traction (L. I. 


W.).... 


0.68 


500 


2f 


.31 


.08 


200 


21' 


X 20' 


Condensing (L. 


L W.) 


3-30 


4000 


5i 


.09 


.04 


206 



*The 12" X 18" automatic engine was new, and gave, throughout, an ex- 
cessive amount of friction as compared with the older engines of the same class 
and make. 



404 THERMODYNAMICS OF THE STEAM-ENGINE. 

The large amount of work absorbed by the main bearings 
and the large coefficient of friction appear the more remark- 
able from the fact that the coefficient of friction for car-axle 
journals is often as low as one tenth of one per cent, the differ- 
ence being probably due to the difference in the methods of 
lubrication. 

The second and obvious conclusion from Table XLI is 
that the valve should be balanced, and that nine tenths of the 
friction of an unbalanced slide-valve is unnecessary waste. 

The friction of the piston and piston-rod are always con- 
siderable, but they vary much with the type of the engine, and 
with differences in handling. It is quite possible to change 
the effective power of an engine by screwing up the piston-rod 
stuffing-box too tightly. The packing of both piston and rod 
should be no tighter than is necessary to prevent perceptible 
leakage, and is more likely to be too tight than too loose. 



CHAPTER XX. 

COMPRESSED AIR. 

Compressed air, that is, air at a pressure above that of the 
atmosphere, is employed for transmitting power from a place 
where it is conveniently generated to places where it is to be 
used. The air-blast used in the production of iron and steel is 
compressed air of moderate pressure ; the compressors for such 
work are called blowing-machines or blowers. Currents of air 
at slightly greater pressure than that of the atmosphere are 
used for ventilating mines, buildings, ships, etc., and for pro- 
ducing a forced draught for steam-boilers. Such currents are 
commonly produced by fans or centrifugal blowers. Air-pumps 
differ from air-compressors in that they take air from a recep- 
tacle in which the pressure is less than that of the atmosphere, 
compress it, and deliver it against the pressure of the atmos- 
phere. 

Power Expended. — The indicator-diagram of an air-com- 
pressor with no clearance space is represent- 
ed by Fig. 79. Air is drawn in at atmos- 
pheric pressure in the part of the cycle of 
operations represented by dc, in the part 
represented by cb the air is compressed, and 
in the part represented by ba it is expelled F1G.79. 

against the higher pressure. 

If /j is the specific pressure and v^ the specific volume of 
one pound of air at atmospheric pressure, and p^ and v^ corre- 
sponding quantities at the higher pressure, then the work done 
by the atmosphere on the piston of the compressor while air is 

405 




406 THERMODYNAMICS OF THE STEAM-ENGINE. 

drawn in is v^p^. Assuming that the compression curve ch may 
be represented by an exponential curve having the form 

pv*" — p^v^ — const., 

then the work of compression is 

If the compression is adiabatic, then the exponent becomes 

K = ~ = 1.405. 
The work of expulsion from ^ to ^ is 

«=A.(f:)-=«(t)'^. 

The effective work of the cycle is therefore 



W 



Equation (312) gives the work done upon one unit of weight 
of air, and the pressures and volumes are specific pressures and 
volumes. If p,, v,, and T, are the pressure, volume, and 
temperature under standard conditions, i.e., at atmospheric 
pressure and at freezing-point, then v^ may be found from the 
equation 



COMPRESSED AIR. 407 

It is frequently convenient to use, instead of equation (312), 
one for the mean effective pressure that may be found by 
dividing it by v^ , so that we have 




M.E.P..A^,{g;)"-x}. . .(3:3) 

in which /, and p^ may be stated in any convenient units, such 
as pounds on the square inch. 

Effect of Clearance. — The indicator-diagram of an air-com- 
pressor with clearance may be represented by Fig. 80. The 
end of the stroke expelling air is at a, and 
the air remaining in the cylinder expands 
from a to d, till the pressure becomes equal 
to the pressure of the atmosphere before the 
next supply of air is drawn in. The expan- 
sion curve ad may commonly be represented ^^^' ^°' 
by an exponential equation having the same exponent as the 
compression curve cb, in which case the air in the clearance 
acts as a cushion which stores and restores energy, but does 
not affect the work done on the air passing through the cylin- 
der. The work of compressing one unit of weight of air in 
such a compressor may be calculated by aid of equation (312), 
but the equation (313) for the mean effective pressure cannot 
be used directly. 

The principal effect of clearance is to increase the size of the 
cylinder required for a certain duty in the ratio of the entire 
length of the diagram in Fig. 80 to the length of the line dc. 

The mean effective pressure may be calculated as for a 
steam-engine indicator-card, taking account of compression 
and expansion as shown in Fig. 80, or the mean effective 
pressure found by equation (313) may be reduced in proportion 
of the line dc to the length of the diagram in Fig. 80. Or, 
again, the mean effective pressure by equation (313) may be 
used with the volume of air actually drawn in per minute, in 
calculating the horse-power. 

Cooling during Compression. — If heat is not withdrawn 
during compression, the temperature rises according to the law 



408 THERMODYNAMICS OF THE STEAM-ENGINE. 

for adiabatic compression. When the maximum pressure /^ is 
moderate, as in blowing-machines, there is ordinarily no pro- 
vision made for cooHng either the air or the cylinder, and the 
compression curve is approximately the adiabatic for air. 
When the final pressure is considerable, as in the use of com- 
pressed air for transmitting power, the high temperatures pro- 
duced without cooling become troublesome, and, in all but 
small machines, some provision is made for cooling the air, or 
the cylinder, or both. 

The cylinder may be cooled by a water-jacket, and the air 
is at the same time cooled, in some degree, by contact with 
the walls of the cylinder. 

The air is most efficiently cooled by injecting water into 
the cylinder, or by using water freely in the cylinder in some 
form. By this means the final temperature of the air is much 
reduced, and the work of compression is also reduced. An in- 
convenience may sometimes arise from the fact that when 
water is so used the air delivered is nearly if not quite satu- 
rated with moisture. 

Moisture in the Cylinder. — If water is not purposely in- 
jected into the cylinder of the compressor, the moisture in the 
air will depend on the hygroscopic condition of the air drawn 
in by the compressor. Even if the air should be saturated the 
total and the relative amount of moisture in the cylinder will 
be insignificant. Thus at 60° F. the pressure of saturated 
steam is about i of a pound on the square inch, and the weight 
of one cubic foot is about 0.0008 of a pound, while the weight 
of one cubic foot of air is about 0.08 of a pound. If the air is 
not saturated the vapor exerts a less pressure than saturated 
vapor at that temperature, and consequently follows the laws 
of superheated steam ; even if the vapor is at first saturated, it 
is superheated by compression, and then follows the same laws. 
Now the adiabatic equation for superheated steam has been 
shown to be 

so that the only effect of the moisture brought into the cylin- 
der by the air is to slightly diminish the exponent of the equa- 



COMPRESSED AIR. 409 

tion representing the compression curve. This conclusion is 
probably valid when the cylinder is cooled by a water-jacket. 

When water is used freely in the cylinder of a compressor, 
the air is cooled by contact with the water, and by vaporization 
of the water. The quantity of moisture in the air, and conse- 
quently the weight of the mixture of air and vapor in the 
cylinder, varies, and the condition of the air during, and at the 
end of, compression can be determined only when the tem- 
perature, volume, and pressure are known. It is commonly 
assumed that the air is saturated at all times under this con- 
dition. 

Temperature at the End of Compression. — When the 
air in the compressor cylinder is dry or contains only the 
moisture brought in with it, it may be assumed that the mix- 
ture of air and vapor follows the law of perfect gases 

pv p^v^ 
~T "" it' 

which, combined with the exponential equation 

pv- = p,v,\ 



gives 

«-r n- 



T T 



(314) 



from which the final temperature T^ at the end of compression 
may be determined when T^ is known. 

When water is used freely in the cylinder of a compressor 
the final temperature cannot be determined directly. Even if 
it be assumed that the air is always saturated, and if the expo- 
nent for the exponential equation be known, it can be deter- 
mined only by a series of approximations. In experiments 
on air-compressors this temperature should be determined 
directly. 

Contraction after Compression. — Ordinarily compressed 
air loses both pressure and temperature on the way from the 
compressor to the place where it is to be used. The loss of 



410 THERMODYNAMICS OF THE STEAM-ENGINE. 

pressure will be discussed under the head of the flow of air in 
long pipes; it should not be large, unless the air is carried 
long distances. This loss of temperature causes a contraction 
of volume in two ways : first, the volume of the air at a given 
pressure is inversely as the absolute temperature ; second, the 
moisture in the air, whether brought in by the air or supplied 
in the condenser, in excess of that which will saturate the air 
at the lowest temperature in the conduit, is condensed. Provi- 
sion must be made for draining off the condensed water. The 
method of estimating the contraction of volume due to the 
condensation of moisture will be exhibited later in the calcula- 
tion of a special problem. 

Interchange of Heat. — The interchange of heat between 
the air in the cylinder of an air-compressor and the walls of 
the cylinder are the converse of those taking place between 
the steam and the walls of the cylinder of a steam-engine, and 
are much less in amount. The walls of the cylinder are never 
so cool as the incoming air nor so warm as the air expelled ; 
consequently the air receives heat during admission and the 
beginning of compression, and yields heat during the latter 
part of compression and during expulsion. The presence of 
moisture in the air increases this effect. 

Volume of the Compressor Cylinder. — Let a compressor 
making n revolutions or 2n strokes per minute be required to 
deliver V^ cubic units (cubic feet or cubic meters) of air at the 
absolute temperature T^ and against the absolute pressure /g, 
expressed in convenient units, such as pounds on the square 
inch or kilograms on the square centimeter. The volume of 
air drawn in by the compressor per minute at the absolute tem- 
perature T^ and the absolute pressure /, can be calculated by 
the equation 

^ = ^- (315) 

If the compressor has no clearance the volume of the cylin- 
der in cubic feet or cubic meters will be 

2^- • • (316) 



COMPRESSED AIR, 41I 

If the compressor has a clearance, the indicator-diagram 
will be similar to Fig. 80, and the air in the clearance at the 
end of the stroke will expand down to the pressure of the at- 
mosphere before the supply-valve will open. Let the clearance 

be — part of the piston displacement. The air in the clearance 

space will, after expansion from the pressure p^ to the pressure 
/i, occupy 

J. (A)' 

part of the piston displacement. Consequently the piston dis- 
placement will be 



l-+i(f -ii (3.) 



expressed in cubic feet or cubic meters. 

The pressure in the compressor cylinder when air is drawn 
in, is always less than the pressure of the atmosphere, and when 
the air is expelled it is greater than the pressure against which 
it is delivered. From these causes and from other imperfec- 
tions the compressor will not deliver the quantity of air calcu- 
lated from its dimensions, and consequently the volume of the 
cylinder as calculated, whether with or without clearance, must 
be increased by an amount to be determined by experiment. 

Compound Compressors. — When air is to be compressed 
from the pressure p^ to the pressure p^^ but is to be delivered 
at the initial temperature t^ , the work of compression may be 
reduced by dividing it between two cylinders, one of which 
takes the air at atmospheric pressure and delivers it at an in- 
termediate pressure // to a reservoir, from which the other 
cylinder takes it and delivers it at the required pressure p^y 
provided that the air be cooled, at the pressure//, between the 
two cylinders. 

The proper method of dividing the pressures and of propor- 
tioning the volumes of the cylinders so that the work of com- 



412 THERMODYNAMICS OF THE STEAM-ENGINE. 

pression may be reduced to a minimum may be deduced from 
equation (312), when there is no clearance or when the clear- 
ance is neglected. 

The work of compressing one pound of air from the pres- 
sure /j to the pressure // is 

The work of compressing one pound from the pressure // 
to p^ is 

because the air after compression in the first cylinder is cooled 
to the temperature t^ before it is supplied to the second cylin- 
der. The total work of compression is 

M - 1 M -I 

w-=«^.+ fr, = A..^j(A')"+(A)" _2}, (3,8) 

and this becomes a minimum when 

becomes a minimum. Differentiating with regard to //, and 
equating the first differential coefficient to zero, gives 

//^'^/aa (319) 

Since the air is supplied to each cylinder at the tempera- 
ture t^ , their volumes should be inversely as the absolute pres- 
sures p^ and //. 

When air is compressed to a very high pressure it may be 
advantageous to carry on the compression in three or more cyl- 
inders successively, cooling the air on the way from one cylin- 
der to the next. 



COMPRESSED AIR. 413 

Fluid Piston Compressors. — It has been shown that the 

effect of clearance is to diminish the capacity of the compressor, 
consequently it should be made as small as possible. With 
this in view the valves of compressors and blowers are com- 
monly set in the cylinder-heads. Single-acting compressors 
with vertical cylinders have been made with a layer of water 
or some other fluid on top of the piston, which entirely fills the 
clearance space when the piston is at the end of the stroke. 
An extension of this principle gives what are known as fluid 
piston compressors. Such a compressor commonly has a 
double-acting piston in a horizontal cylinder much longer than 
the stroke of the piston, thus giving a large clearance at each 
end. The clearance spaces extend upward to a considerable 
height, and the admission and exhaust valves are placed at or 
near the top, and the entire clearance space is filled with water. 
The spaces and heights must be so arranged that when the 
piston is at one end of its stroke, the water at that end shall 
fill the clearance and cover the valves, and at the other end the 
water shall not fall to the level of the top of the cylinder. 
There are consequently two vertical fluid pistons actuated by 
a double-acting horizontal piston. It is essential that the spaces 
in which the fluid pistons act shall give no spaces in which 
air may be caught as in a pocket, and that there are no pro- 
jecting ribs or other irregularities to break the surface of the 
water ; and, further, the compressor must be run at a moderate 
speed. 

The water forming the fluid pistons becomes heated and 
saturated with air by continuous use, and should be renewed. 
Cooling by a spray of water during compression may be com- 
bined advantageously with the use of this form of piston. 

Air-pumps used with condensing engines, or for other pur- 
poses, may be made with fluid pistons which are renewed by 
the water coming with the air or vapor. In case the water thus 
supplied is insufficient, water from without may be admitted, 
or water from the delivery may be allowed to flow back to the 
admission side of the pump. 



414 THERMODYNAMICS OF THE STEAM-ENGINE. 

Displacement Compressors. — When a supply of water 
under sufficient head is available, air may be compressed in 
suitably arranged cylinders or compressors by direct action of 
the water on air, compressing it and expelling it by displace- 
ment. 

Rotary Blowers. — Rotary blowers have one or more rotat- 
ing parts or pistons, so arranged that as they rotate chambers 
of varying capacity are formed, which receive the air at atmos- 
pheric pressure, compress it and deliver it against the higher 
pressure. No attempt is made to cool the air, and the clear- 
ance should be zero, so that the work of compression may be 
calculated by equation (312) with /^ — /<• = 1.4. 

Fan Blowers. — The complete theory of centrifugal and 
other rotating fans cannot be deduced from thermodynamics 
alone. The work done upon the air may, however, be calcu- 
lated as follows : Let the pressure and velocity of the air ap- 
proaching the fan be p^ and u^ , and of the air leaving the fan 
/>2 and u^. Then the intrinsic energy under the initial and final 
conditions will be, by equation (84), 



K — \ 



and the kinetic energy of one pound under the same conditions 
will be ^~ 



so that the work done on the air will be 

or, substituting for v^ from the equation p^v^^ = A^a*> 






2g K—l 



COMPRESSED AIR. 



415 



Tests of Compressors. — From a large number of tests on 
fluid-piston air-compressors constructed by the Cockerill Works, 
Seraing, for use at the Mont Cenis tunnel, Mr. John Kraft* 
has compiled the following table : 

Performance of Fluid Piston in Compressors. 





Volume of the cylinder to 

deliver on cubic meter of 

compressed air. 


Work of compression, 
kilogrammeters. 




Friction of pis- 
ton and piston- 
rod. 


B 


(0 


Required to 
compress air 
drawn in, at 
constant tem- 
perature. 


Required to 
compress con- 
tents of cylin. 
at constant 
temperature. 


ill 


Loss from heat- 
ing in per 
cent of col- 
umn 6. 


^1 

< 


Volume of 
air drawn 
in cubic 
meters. 


Piston dis- 
placement, 
cubic 
meters. 


Loss of vol. 
in per cent 
of piston 
displacem't. 


Work applied 
to compres- 
sor through 
dynamomet. 


c c c 
^B. 


c S 

"0 3 


1 

2 

3 
4 
5 
6 


2 

2 
3 
4 
5 
6 


3 

2.222 
3-333 
4-444 

5-555 
6.666 


4 

10 
10 
10 
10 
10 


5 

14320 
34046 
57282 
83127 
II 1053 


6 

15912 
37829 
63646 
92364 
123393 


7 

17185 
43503 

155675 


8 

8 
15 
20 
23 
26 


9 

26293 
52204 
89360 
124969 
171023 


10 

53 
20 

17 
10 
10 


11 

0.544 
0.652 
0.647 
0.665 
0.649 



The first column gives the absolute pressure of the com- 
pressed air delivered by the compressor in atmospheres. The 
second column gives the volume of air that must be drawn in 
by the compressor to deliver one cubic meter, on the assump- 
tion that the air is cooled after compression to the original 
temperature. The third column gives the piston displace- 
ment actually required ; this is larger than the volume in col- 
umn 2, because [a) the pressure in the cylinder while the cylin- 
der is filling is less than that of the atmosphere ; {U) the air is 
heated as it is drawn into the cylinder ; {c) the water forming 
the fluid piston absorbs air at high pressures and gives it up at 
low pressures ; {d) some water is injected at each stroke ; {e) 
the air during expulsion has a higher pressure in the cylinder 
than that against which the air is expelled. The total loss 
from this source, set down in column 4, was determined by 
numerous experiments. Column 5 gives the work that would 
be required to deliver one cubic meter of air if there were no 
loss or imperfection, and if the air were maintained at the origi- 
nal temperature during compression. Column 6 gives the work 

* Revue universelle des Mines, 2 S6rie, Tome vi. p. 301. 



4i6 



THERMODYNAMICS OF THE STEAM-ENGINE. 



required on the assumption that ten per cent of the piston dis- 
placement is lost. Column 7 gives the indicated work done on 
the contents of the cylinder for each cubic meter of air deliv- 
ered. The loss from the failure to prevent heating during: 
compression is given in column 8. Column 9 gives the work 
expended on the compressor for each cubic meter of air deliv- 
ered, determined by experiments on a Prony brake. The loss 
from friction in per cent of the indicated work is given in col- 
umn 10. Column II gives the ratio of column 5 to column 9, 
which is the efficiency of the compressor if it is required to de- 
liver air at the original temperature. 

For convenience, Mr. Kraft gives the distribution of the 
work applied to the compressor in the following table : 

DISTRIBUTION OF WORK APPLIED TO AIR-COMPRESSOR. 



Pressure 

in 

Atmospheres. 


Useful Work. 


Loss from 

Heating- during 

Compression 


Loss from 

Imperfections of 

Cycle. 


Loss 
from Friction. 


I. 


2. 


3- 


4. 


5- 


2 

3 

4 
5 
6 


0.544 
0.652 
0.647 
0.665 
0.649 


0.0485 
0.1087 
0.1427 
0.1702 
0.1880 


0.0600 
0.0724 
0.0712 
0.0732 
0720 


0.3465 
0.1666 

1434 
. 0903 
0.0910 



Pernolet* gives the following test of a blowing-engine used 
to produce the blast for Bessemer converters at Creusot. The 
engine was a two-cylinder horizontal engine, with the cranks 
at right angles. The piston-rod for each cylinder extended 
through the cylinder-head, and actuated a double-acting com- 
pressor. The dimensions were : 

Diameter, steam-pistons, 1.2 meters. 

" air-pistons, 1.5 " 

Stroke, 1.8 " 

Diameter of fly-wheel, 8.0 " 



L'Air Comprime, 1876. 



COMPRESSED AIR. 417 

At 28 revolutions per minute the following results were 
obtained : 

Indicated horse-power of steam-cylinders, 1082 

" " of air-cylinders, 999 

Efficiency, 0.92 

Temperature of air admitted, 10° C. 

'' '' delivered, 60° C. 

Pressure of air delivered, meters of mercury above the 

atmosphere, 1.2 1 

Pressure of air in supply-pipe, meters of mercury below 

the atmosphere, 0.023 

At 25 revolutions there was no sensible depression of pres- 
sure in the supply-pipe. 

The air from such a blowing-engine probably suffers little 
loss of temperature after compression. 

Air-pumps. — The feed-water supplied to a steam-boiler 
usually contains air in solution, which passes from the boiler 
with the steam to the engine and thence to the condenser. In 
like manner the injection-water supplied to a jet condenser 
brings in air in solution. Also, there is more or less leakage of 
air into the cylinder communicating with the condenser, and 
into the exhaust-pipe, or the condenser itself. An air-pump 
must therefore be provided to remove this air and to maintain 
the vacuum. The air-pump also removes the condensed steam 
from a surface condenser, and the mingled condensed steam 
and injection-water from a jet condenser. If no air were 
brought into the condenser, the vacuum would be maintained 
by the condensation of the steam by the injection, or the cool- 
ing water, and it would be sufficient to remove the water by a 
common pump ; which, with a surface^condenser, might be the 
feed-pump. 

The weight of injection-water per pound of steam, calcu- 
lated by the method on page 196, will usually be less than 20 
pounds, but it is customary to provide 30 pounds of injection- 
water per pound of steam, with some method of regulating the 
quantity delivered. 



4i8 



THERMODYNAMICS OF THE STEAM-ENGINE, 



It may be assumed that the injection-water will bring in 
with it one twentieth of its volume of air at atmospheric pres- 
sure, and that this air will expand in the condenser to a volume 
inversely proportional to the absolute pressure in the con- 
denser. The capacity of the air-pump must be sufficient to 
remove this air, and the condensed steam and injection-water. 

An air-pump for use with a surface condenser may be 
smaller than one used with a jet condenser. In marine work it 
is common to provide a method of changing a surface into a 
jet condenser, and to make the air-pump large enough to give 
a fair vacuum in case such a change should become advisable 
in an emergency. 

Seaton"^ states that the efficiency of a vertical single-acting 
air-pump varies from 0.4 to 0.6, and that of a double-acting 
horizontal air-pump from 0.3 to 0.5, depending on the design 
and condition ; that is, the volume of air and water actually 
discharged will bear such ratios to the displacement of the 
pump. 

He also gives the following table of ratios of capacity of 
air-pump cyHnders to the volume of the engine cylinder or 
cylinders discharging steam into the condenser : 

RATIO OF ENGINE AND AIR-PUMP CYLINDERS. 



Description of Pump. 



Single-acting vertical 



Double-acting horizontal . 



Description of Engine. 



Jet-condensing, expansion i^ to 2 
S r ice- " " i^ to 2 

JeL- " " 3 to 5 

Surface- ** " 3 to 5 

" " compound 

Jet-condensing, expansion i^ to 2 

Surface- " " i| to 2 

Jet- " " 3 to 5 

Surface- " " 3 to 5 

" " compound 



Ratio. 



6 to 8 

8 to 10 

10 to 12 

12 to 15 

15 to 18 
10 to 13 

13 to 16 

16 to 19 
19 to 24 
24 to 28 



Calculation of an Air-compressor. — Let it be assumed 
that an air-compressor delivers 100 cubic feet of air at a pres- 



* Manual of Marine Engineering. 



COMPRESSED AIR. 419 

sure of 50 pounds by the gauge and at 80° F.; also, that the 
temperature of the air suppHed to the compressor is 60° F., that 
the pressure of the atmosphere is 14.7 pounds, and that there 
is a loss between the compressor and the point of delivery of 
two pounds of pressure. 

The compressor must draw in per minute 

100 X 64.7 X 520.7 ^. . ^ 

= 424 cubic feet. 

14.7 X 540.7 

The actual capacity of a fluid-piston compressor is stated to 
be 0.9 its apparent capacity, so that such a compressor would 
have for its apparent capacity per minute 

424 -^ 0.9 = 47 1. 1 cubic feet. 

Assuming 20 revolutions or 40 strokes per minute, the 
piston displacement will be 

471. 1 -^ 40 = 1 1.8 cubic feet, 

or the piston may have a diameter of 24i inches, and a stroke 
of 4 feet. 

A dry-air compressor will deliver less than the calculated 
amount of air on account of imperfect action of the valves, 
heating of the air as it enters, etc.; but there will be no water 
injected, and consequently none to expel. For comparison 
with the calculation for the fluid-piston compressor we will as- 
sume the actual delivery to be 0.92 of the calculated delivery, 
allowing for clearance. Consequently the apparent delivery of 
a compressor taking 424 cubic feet per minute must be 

424 -^ 0.92 — 460.9 cubic feet. 

If the clearance is 0.02 of the piston displacement, then the 
air in the clearance at 66.7 pounds absolute pressure will 
occupy 

0.02 = 0.0589 

V14.7/ 



420 THERMODYNAMICS OF THE STEAM-ENGINE. 

of the piston displacement at 14.7 pounds pressure. The 
piston displacement must consequently be 

I + 0.0589 — 0.02 = 1.0389 

times the displacement for a similar compressor without clear- 
ance. The piston displacement per minute will be 

460.9 X 1.0389 = 478.8 cubic feet. 

Assuming the compressor to make 60 revolutions per minute, 
the piston displacement will be 

478.8 -^ 120 == 4 cubic feet, 

or the piston may have a diameter of i ^\ inches and a stroke 
of 3 feet. 

The exponent of the equation representing the compres- 
sion curve for the fluid-piston compressor may be assumed to 
be 1.2, so that the mean effective pressure will be 



1.2 ( /66.7\ ^-^ 
H-7 X ^^^^ { (— ) - U = 25.3, 



and the indicated horse-power will be 

25.3 X 471-1 X 144 ._ 
33000 ~ 



52.0 H.P. 



The mean effective pressure for a dry-air compressor with- 
out clearance will be 

1-4- I 

'4-7 X i:^ 1 (7^) -A= -7.8, 

and the indicated horse-power will be 

27.8 X 460.9 X 144 ,,^TTp 

=55.0 H.r. 

33000 ^^ ^ 



COMPRESSED AIR. 42 1 

A dry-air compressor with a clearance will have a larger 
piston displacement, but will absorb no more power, since the 
work stored and restored by the air in the clearance space does 
not affect the power required to deliver the given amount of 
compressed air. 

According to Kraft's table, on page 416, the friction of an 
air-compressor for a^\ atmospheres is about 10 per cent of the 
gross power expended. Consequently the gross power re- 
quired to produce 100 cubic feet of air by use of a fluid-piston 
compressor is 

52.0 -^ 0.90 — 57.8 H. P. 

If the compressor is made with the piston on the same rod 
as the piston of a steam-engine cylinder, so that engine and 
compressor form one machine, then it may be assumed that 15 
per cent of the indicated horse-power of the engine will be ab- 
sorbed by the friction of the machine, and the indicated horse- 
power of the engine will be 

52.0-^0.85 = 61.2 H.P. 

The temperature of the air delivered by the dry-air com- 
pressor, found by the equation (314), will be 



^ /66.7\ '-4 

^^=52o.7y) =802.1; 

.-./,=: 802.1 — 460.7 = 341 °.4 F. 

If the substance in the cylinder of the fluid-piston compres- 
sor followed the law of perfect gases, then for it the final 
temperature would be 



7;= 520.7 --t) =669.9; 
\I4.// 

.-./, = 669.9 — 460.7 — 209°. 2 F. 



422 THERMODYNAMICS OF THE STEAM-ENGINE. 

But the final temperature cannot be found in this way, since 
water is vaporized in the cylinder during compression and tl\e 
weight of the substance operated on is not constant. Now 
one cubic foot of air at the pressure of 14.7 pounds will, after 
compression, occupy 






0.2836 



of one cubic foot. If the temperature 209". 2 be assumed to 
be the final temperature, and it further be assumed that the 
air is saturated at that temperature after compression, then 
the pressure exerted by the vapor will be 13.87 pounds, and 
the pressure exerted by the air will be 

66.^ — 13.87 = 52.83 pounds. 

But one cubic foot of air at 14.7 pounds pressure and at 
60° F. will at 52.8 pounds pressure and at 209°. 2 F. occupy 

'4-7 X 669.9 _ 

52.8 X 520.8 - °-35^^ 

of a cubic foot. Consequently it cannot be that the air after 
compression is saturated with moisture at 209°. 2 F. 

Suppose the temperature of the moist air after compression 
to be 165° F., then the condition of the air may be found as 
follows : The pressure exerted by the air will be 

14.7 X 625.7 . 
520.7 X 0.28 ^ = ^^-'9 pounds, 

and the pressure exerted by the vapor of water will be 

^6.^] — 62.29 — 4-4^ pounds, 

while the pressure of saturated vapor at that temperature is 
5.45 pounds. The weight of one cubic foot of superheated 
steam at the pressure of 4.41 pounds per square inch, or 635 
pounds per square foot, and at the absolute temperature of 



COMPRESSED AIR. 423 

625°. 7, may be found by aid of equation (184), for superheated 
steam, to be 0.0118 of a pound. Assuming the weight of the 
vapor at the temperature of 165° F. to be proportional to the 
pressure, gives 

0.01449 X 44 ■ 



5.324 



= 0.012 pound. 



which is a sufficient approximation. 

Had the temperature been assumed to be 161° F., a similar 
calculation would give for the pressure of the air 61.88 pounds, 
and for the vapor 4.82 pounds, while the pressure of saturated 
vapor at that temperature is 4.84 pounds ; that is, the air 
would be saturated with vapor at that temperature. 

The greater part of the vapor in the air at the pressure of 
52 pounds by the gauge and at 165° F. will be condensed 
before the air arrives at the end of the conduit, where the 
pressure is supposed to be 50 pounds and the temperature 80° 
F. The volume of air delivered per minute is 

424 X 0.2836 = 120.2 

cubic feet, which by the previous calculation contains 0.012 
pound of moisture per cubic foot, or, in all, 

120.2 X 0.012 = 1.44 pounds. 

The 100 cubic feet at 80° F. if saturated will contain 

100 X 0.001553 = 0.16 pound, 

so that the water condensed per minute is, for 100 cubic feet, 

1.44 — 0.16 = 1.28 pounds. 

Had the temperature at the point of delivery been the same 
as that of the air supplied to the compressor, as is common in 
practice, then nearly all the vapor in the air after compression 
would have been condensed and withdrawn. 

When necessary, the contraction of volume after compres- 
sion on account of the loss of temperature and accompanying 



424 THERMODYNAMICS OF THE STEAM-ENGINE. 

condensation of moisture may be calculated as follows : The 
pressure exerted by the air was found to be 62.29 pounds, and 
that exerted by the vapor to be 4.41 pounds. If the moisture 
were entirely withdrawn at 165°, the air would then exert the 
entire pressure of ^d.'j pounds, and its volume would be 

120.2 X 62.29 , . ^ 
-^z = 1 12.3 cubic feet. 

But at the final temperature of 80° the pressure of saturated 
vapor is 0.5027 of a pound, so that the air exerts a pressure of 

50 + 147 — 0.50 = 64.2 pounds, 

and its volume will be 

1 12.3 X 540.7 X 64.2 



625.7 X 62.29 



= 100 cubic feet. 



In this case the calculation gives, as it should, the original 
datum of the problem, and the calculation is inserted to show 
the method only. Obviously the final volume of the air 
delivered by a given compressor, at a given temperature and 
pressure, may be calculated from the volume drawn into the 
compressor without calculating the volume delivered at the 
pressure and temperature near the compressor. 

If a so-called dry-air compressor draws air from the atmos- 
phere, and the air is finally used at or near the original tem- 
perature of the atmosphere, then that air will ordinarily be 
saturated. In the problem given, the air suppHed to the com- 
pressor per minute, if half saturated, will contain 

424 X 0.0008104 

2_:r 7_ 0.172 

2 ' 

pound of moisture. If the air is cooled again to 60°, it can 
contain, when saturated, 

100 X .0008104 = 0.081 



COMPRESSED AIR, 



425 



pound of moisture, and the remainder will be condensed. 
Even at the temperature of 80°, 100 cubic feet of saturated air 
will contain only 

100 X 0.001553 =0.155 

pound of moisture, so that the air will, under the suppositions, 

be saturated, and some moisture will be condensed. 

Compressed-air Engines. — Engines for using compressed 

air differ from steam-engines only in details that depend on the 

nature of the working fluid. In some instances compressed air 

has been used in steam-engines without any change ; for ex- 
ample, in Fig. 81 the dotted diagram was taken from the 

cylinder of an engine using 

compressed air, and the 

dot-and-dash diagram was 

taken from the same end 

of the cylinder when steam 

was used in it. The full 

line ab is a hyperbola, and 

the line ac is the adiabatic 

line for a gas drawn 

through the intersection of the expansion 

diagrams. 

Power of Compressed-air Engines. — The probable mean 

effective pressure attained in the cylinder of a compressed-air 
engine, or to be expected in a projected 
engine, may be found in the same manner 
as is used in designing a steam-engine. In 
Fig. 82, the expansion curve i, 2 and the 
compression curve 3, may be assumed to be 

adiabatic lines for a gas represented by the equation 




Fig. 8x. 

lines of 



the two 




Fig. 82. 



and the area of the diagram may be found in the usual way, 
and therefrom the mean effective pressure can be determined. 
Having the mean effective pressure, the power of a given engine 



426 THERMODYNAMICS OF THE STEAM-ENGINE. 

or the size required for a given power may be determined 
directly. 

Let the specific pressure and the specific volume in the 
supply-pipe be/3 and v^^ and let the specific pressure and the 
specific volume in the exhaust-pipe be p^ and v^ ; then, assum- 
ing that there are no losses of pressure in the valves and 
passages, that there is no clearance, and that the expansion is 
adiabatic, the work of one unit of weight of air is 

or, in terms of the final pressure and volume, 

»'.=a%;^|(a)"'^'-'|- • • (322) 

When it is more convenient, the mean effective pressure 
can be obtained by aid of the equation 

M.E.P.=A;^jg)'^-.|, . . (323) 

in which the pressures may be in any convenient units, as, for 
example, in pounds on the square inch. 

If an engine fulfils all of the above conditions except that 
there is a clearance, then equations (321) and (322) maybe used 
for finding the work developed by one unit of weight of air, 
provided that the clearance is filled by compression, with air at 
the admission pressure /g. The equation (323) for the mean 
effective pressure cannot be used directly, but it may be used 
in connection with the volume exhausted per stroke or per 




COMPRESSED AIR. 427 

minute, in calculating the power of the engine. The diagram 
from such an engine will be represented by Fig. Z^^ and the 
foregoing statement may be put in the fol- 
lowing form : The actual mean effective pres- 
sure is the mean effective pressure by equa- 
tion (323), multiplied by the ratio of the line 
cd to the entire length of the diagram. It is 
apparent that the only effect of clearance ^'°- ^3- 

is to increase the size of cylinder required for a given purpose, 
and with it the work lost in friction. 

Air Consumption.-— The air consumed by a given com- 
pressed-air engine may be calculated from the volume, pressure, 
and temperature at cut-off or release, and the volume, tempera- 
ture, and pressure at compression, in the same way that the 
indicated consumption of a steam-engine is calculated ; but in 
this case the indicated and actual consumption should be the 
same, since there is no change of state of the working fluid. 
Since the intrinsic energy of a gas is a function of the tempera- 
ture only, the temperature will not be changed by loss of 
pressure in the valves and passages, and the air at cut-off will 
be cooler than in the supply-pipe, only on account of the 
chilling action of the walls of the cylinder during admission, 
which action cannot be energetic when the air is dry, and 
probably is not very important when the air is saturated. 

Final Temperature. — If the expansion in a compressed- 
air engine is complete, i.e., if it is carried down to the pressure 
in the exhaust-pipe, then, assuming that there are no losses of 
pressure in valves and passages, the final temperature may be 
found by the equation 

If the expansion is not complete, then the temperature at 
the end of expansion may be found by the equation 






(325) 



428 THERMODYNAMICS OF THE STEAM-ENGINE. 

\\\ which V^ is the volume in the cyHnder at cut-off and Vr at 
release, T^ is the absolute temperature at the end of expan- 
sion, and 7*3 is the temperature at cut-off, assumed to be the 
same as in the supply-pipe. T^ is not the temperature during 
back pressure nor in the exhaust-pipe. If the exhaust-valve 
is opened suddenly at release the air will expand suddenly, and 
part of the air will be expelled at the expense of the energy in 
the air remaining — much as though that air expanded behind a 
piston and the temperature in the cylinder during exhaust, and 
at the beginning of compression, may be calculated by equation 
(325). The temperature in the exhaust-pipe will not be so 
low, for the temperature of the escaping air will vary during 
the expulsion produced by sudden expansion, and will only at 
the end of that operation have the temperature T^, while the 
energy expended on that air to give it velocity will be restored 
when the velocity is reduced to that in the exhaust-pipe. 

Volume of the Cylinder. — The determination of the 
volume of the cylinder of a compressed-air engine, which uses a 
stated volume of air per minute, is the converse of the determi- 
nation of the air consumed by a given engine, and can be found 
by a similar process. We may calculate the volume of air at 
the pressure in the supply-pipe, consumed per stroke by an 
engine having one unit of volume for its piston displacement, 
and therefrom find the number of units of volume of the piston 
displacement for the required engine. 

Interchange of Heat. — The interchanges of heat between 
the walls of the cylinder of a compressed-air engine and the air 
working therein are of the same sort as those taking place 
between the steam and the walls of the cylinder of a steam- 
engine ; that is to say, the walls absorb heat during admission 
and compression, if the latter is carried to a considerable 
degree, and yield heat during expansion and exhaust. Since 
the walls of the cylinder are never so warm as the entering air, 
nor so cold as the air exhausted, the walls may absorb heat 
during the beginning of expansion, and yield heat during the 
beginning of compression. 

The amount of interchange of heat is much less in a com- 



COMPRESSED AIR. 429 

pressed-air engine than in a steam-engine. With a moderate 
expansion, the interchanges of heat between dry air and the 
walls of the cylinder are insignificant. Moisture in the air in- 
creases the interchanges in a marked degree, but does not make 
them so large that they need be considered in ordinary calcu- 
lations. 

Moisture in the Cylinder. — The chief disadvantage in the 
use of moist compressed air — and it is fair to assume that com- 
pressed air is nearly if not quite saturated when it comes to 
the engine — is that the low temperature, experienced when 
the range of pressures is considerable, causes the moisture to 
freeze in the cylinder and clog the exhaust-valves. The dififi- 
culty may be overcome in part by making the valves and 
passages of large size. Freezing of the moisture may be pre- 
vented by injecting steam or hot water into the supply-pipe or 
the cylinder, or the air may be heated by passing it through ex- 
ternally heated pipes, or by some similar device. In the appli- 
cation of compressed air to driving street-cars the air from the 
reservoir has been passed through hot water, and thereby 
made to take up enough hot moisture to prevent freezing. 
The study of gas-engines suggests a method of heating com- 
pressed air which it is believed has never been tried. The air 
supplied to a compressed-air engine, or a part of the air, could 
be caused to pass through a lamp of proper construction to 
give complete combustion, and the products of combustion 
passed to the engine with the air. Should such a device be 
used, it would be advisable that the temperature of the air 
should be raised only to a moderate degree to avoid destruction 
of the lubricants in the cylinder, and the combustion at all 
hazards must be complete, or the cylinder would be fouled by 
unburned carbon. 

Compound Air Engines.— When air is expanded to a 
considerable degree in a compressed-air engine a gain may be 
realized by dividing the expansion into two or more stages in 
as many cylinders, provided that the air can be economically 
reheated between the cylinders. The heat of the atmosphere 
or of water at the same temperature may sometimes be used 



430 THERMODYNAMICS OF THE STEAM-ENGINE. 

for this purpose. It is not known that machines of this con- 
struction have been used. If they were to be constructed, the 
practical advantages of equal distribution of work and pressure 
would probably control the ratio of the volumes of the cylinders. 

Calculation of a Compressed-air Engine. — Suppose that 
a compressed-air engine has a diameter of lO inches and a 
stroke of 20 inches, that it makes 100 revolutions per minute, 
and is supplied with air at 80° F. and at 50 pounds gauge- 
pressure. Let the cut-off be at one-half stroke, the compression 
at 5 per cent of the stroke, and the clearance 5 per cent of the 
piston displacement. 

The pressure at the end of expansion will be 



64-7 X@"= 25.8 



pounds absolute, or 11. 12 pounds above the atmosphere. The 
pressure at the end of compression will be 

, '47 X(—) =38.8 

pounds absolute, or 24.1 pounds above the pressure of the at- 
mosphere. 

The mean effective pressure will be 



M. E. P. = 64.7 X 0.5s + 64.7 X (o-SSy V0.55 ^ ~ ^47 X 0.95 

/»o.i dv 
-i4.7X(o.i)-X^-; 

. • . M. E. P. = 32.35 + 20.50 — 13.97 — 1.94 = 36.94. 

If the engine has large ports and automatic cut-off valves 
the mean effective pressure realized may be assumed to be 0.95 
of that calculated, or it will be about 35 pounds. 

Assuming the diameter of the piston-rod to be 2 inches, the 
mean area of the piston will be 

2X78-54— 3-14 . , 
= J^j square mches. 



COMPRESSED AIR. 43 1 

The horse-power will therefore be 
35 X 77 X 2 X lOO X 20 



33000 X 12 



3.6 I. H. P. 



If, further, the friction of the engine is assumed to absorb 
one tenth of the indicated horse-power, the efTective horse- 
power will be \2\. 

The temperature of the air at the end of expansion will be 

540.7 x(^—j =417.5; 

or — 42°. F. The temperature at the beginning of compression 
may be assumed to be 



54°-7x(g|)- =354.1; 



or — 106° F. The influence of moisture in the air and of the 
interchanges of heat will be to increase each of these tempera- 
tures. 

Were it desired to prevent freezing in the cylinder, then the 
lowest temperature must be at least 32° F., and the entering 
air should have at least the temperature of 



(^ 0.4 



or 243°.6 F. It is probable that a less temperature than this 
will obviate difficulty from freezing. 

The piston displacement of the engine will be 

77 X 20 

PT" = o.8qi cubic foot. 

1728 ^ 

The volume of air caught in the cylinder at compression 
will be 0.089 ^^ ^ cubic foot at the pressure of 14.7 pounds, and 
at the absolute temperature, as calculated, of 354.1. At the 



432 THERMODYNAMICS OF THE STEAM ENGINE. 

temperature 80° F., and at 64.7 pounds absolute pressure, the 
volume will be 

540.7 14.7 

0.089 X X z— ^ = 0.031 cubic foot. 

^ 354.1 64.7 ^ 

Consequently the air consumed per stroke will apparently be 

0.55 X 0.891 — 0.031 = 0.459 

of a cubic foot. But the causes which prevent the realization 
of the mean effective pressure diminish the consumption of 
air, so that the consumption per stroke may be assumed to be 

0.95 X 0.459 ^ 0436 

of a cubic foot. The consumption per minute will therefore be 
2 X 100 X 0.436 = 87.2 cubic feet. 

Were it required that a compressed-air engine should use 
100 cubic feet of air per minute, the piston displacement w^ould 
obviously be 1.02 cubic feet, and the indicated horse-power 
would be 15.6, while the effective horse-power would be 14. 
Comparing this result with the power expended on the fluid- 
piston air-compressor, it appears that the efficiency of the fluid is 

15.6 -^ 52.0 — 0.30, 

while the efficiency of the whole apparatus for transferring 
power is 

14 -f- 57.8 — 0.24. 

Efficiency of Compressed-air Transmission. — The great 
defect of compressed air as a means of transmitting power, that 
is, the small per cent of work realized, is exhibited by the pre- 
ceding calculation. Though a greater efficiency may be at- 
tained by a better choice of pressures and proportions, the 
result will in all cases be unsatisfactory. Compressed air for 
this purpose is consequently employed only where power for 
compression is cheap and abundant, or where there are special 



COMPRESSED AIR. 433 

reasons for using air. As an example, compressed air is used 
in mining and tunnelling where the use of steam would be 
objectionable. It is suggested that compressed air may be used 
in operating cranes where hydraulic power is objectionable from 
the liability of freezing water-pipes, and where there is a 
large loss from condensation of steam in starting and operating 
only a short time. 

Experiments made by M. Graillot* of the Blanzy mines 
showed an efficiency of from 22 to 32 per cent. Experiments 
made by Mr. Daniel at Leeds gave an efficiency varying from 
0.255 to 0.455, ^^'ith pressures varying from 2.75 atmospheres to 
1.33 atmospheres. An experiment made by Mr. Kraft f gave 
an efficiency of 0.137 for a small machine, using air at a pressure 
of five atmospheres without expansion. 

*Pernolet, L'Air Comprime, pp. 549, 550. 

f Revue universelle des Mines, 2 Serie, Tome vi. 



CHAPTER XXI. 



REFRIGERATING MACHINES. 



In the discussion of heat-engines it appeared that the sim- 
plest cycle described by such an engine is that for Carnot's 

ideal engine, represented by Fig. 84. 
When the working substance in the 
cylinder P is a gas the cycle represented 
by Fig. 85 is composed of two isother- 

1 mal lines, AB and CD, and of two adi- 

' abatic lines, BC and DA. When the 
working substance is a mixture of a 
liquid and its vapor, the two isothermal lines become parallel 
to the axis OV, but the order of events is in no wise altered. 

When working direct, Carnot's engine takes from the source 
of heat A a quantity of heat g, changes a part into mechani- 
cal energy, and rejects the remainder Q^ to the refrigerator B, 
The efficiency 



L_l Q LJ 

Fig. 84. 



77 = 



AW Q-Q, T 



Q 



Q 



increases with the difference of temperatures of the source of 
heat and the refrigerator. 

If the engine be reversed so that it describes the cycle in 
the order ADCBA, it takes heat from the re- 
frigerator, adds thereto the heat equivalent of 
the work of the cycle, and delivers the sum to 
the source of heat, and thus becomes a refrig- 
erating machine. It is apparent that in this 
action it is desirable to do as little work as pos- 
sible on the working substance, and that this 
condition is fulfilled by making the difference of temperatures 
as small as possible. 

434 




Fig. 85. 



REFRIGERATING MACHINES. 435 

In practice it is found convenient to supply to a heat-engine 
at each stroke a quantity of the working substance at a high 
temperature, which does work on the piston, and is rejected at 
a lower temperature. Thus the steam-engine takes steam from 
the boiler which serves as a source of heat, and, after abstract- 
ing some of the heat in the form of work, rejects the steam to 
the condenser or refrigerator. In like manner refrigerating 
machines take a supply of the working substance from the re- 
frigerator or refrigerant, do work upon it, and deliver it at a 
higher temperature to a receptacle which is known as the cooler 
or condenser, but which takes the place of the source of heat 
or boiler. 

Two forms of refrigerating machines are in common use — 
air -refrigerating machines and compression -refrigerating ma- 
chines using a saturated vapor — such as the ammonia-refriger- 
ating or ice-machine. 

Air-refrigerating Machine. — The general arrangement of 
an air-refrigerating machine is shown by Fig. 86. It consists 
of a compression cylinder^, an expansion cylinder B of smaller 
size, and a cooler C. It is commonly used to keep the atmos- 
phere in a cold storage-room at a low temperature, and has cer- 
tain advantages for this purpose, especially on shipboard. The 
air from the storage-room comes to the compressor at or about 
freezing-point, is compressed to two or three atmospheres and 
delivered to the cooler, which has the same form as a surface con- 
denser, with cooling water entering at e and leaving at /. From 
the cooler the air, usually somewhat warmer than the atmos- 
phere, goes to the expansion cylinder B, in which it is expanded 
nearly to the pressure of the air and cooled to a low temperature, 
and then delivered to the storage-room. The inlet valves 
a^ a and the delivery-valves b, b of the compressor are 
moved by the air itself ; the admission-valves ^, c and the ex- 
haust-valves d, d of the expansion cylinder are like those of a 
steam-engine, and must be moved by the machine. The differ- 
ence between the work done on the air in the compressor, and 
that done by the air in the expansion cylinder, together with 



436 



THERMODYNAMICS OF THE STEAM-ENGINE. 



the friction work of the whole machine, must be suppHed by a 
steam-engine or other motor. 

The effect of clearance in the compression cylinder, as has 
been seen in the discussion of air-compressors, is to increase 
the size required for a certain performance. The exhaust-valves 
of the expansion cylinder should be so set that the clearance 



..^-^^ 




Fig. 86. 

shall be filled by compression with air at nearly if not quite the 
admission pressure, and the cut-off should be such that the air 
shall expand down to the back pressure. This latter is always 
of importance for the efficient action of the machine, but if the 
clearance is small the compression is of less moment. 

It is customary to provide the compression cylinder with a 
water-jacket to prevent overheating, and frequently a spray of 
water is thrown into the cylinder to reduce the heating and the 



REFRIGERATING MACHINES. 43/ 

work of compression. Sometimes the cooler C^ Fig. 86, is re- 
placed by an apparatus resembling a steam-engine jet condenser, 
in which the air is cooled by a spray of water. In any case it is 
essential that the moisture in the air, as well as the water injected/ 
should be efficiently removed before the air is delivered to the 
expansion cylinder, otherwise snow will form in that cylinder 
and interfere with the action of the machine. Various mechani- 
cal devices have been used to collect and remove water from 
the air, but air may be saturated with moisture after it has 
passed such a device. The Bell-Coleman Company use a jet 
cooler with provision for collecting and withdrawing water, and 
then pass the air through pipes in the cold room on the way to 
the expansion cylinder. The cold room is maintained at a tem- 
perature a little above freezing-point, so that the moisture in 
the air is condensed upon the sides of the pipes and drains back 
into the cooler. The same machine, as made by Menck and 
Hambrock, is provided with a device for removing moisture 
from the air, that is shown by Fig. 87. Air from the cooler 
comes in by the pipe a, is distributed by the annular perforated 
pipe b, and passes out to the expansion cylinder by the pipe c. 
The chamber E is surrounded by a jacket through which passes 
the cold air on the way from the expansion cylinder to the 
cold room. Since the air in the jacket is many degrees below 
freezing-point the walls of the chamber E are quickly covered 
with frost, which accumulates till a considerable thickness is at- 
tained ; afterwards the moisture condenses and runs down to 
the bottom of the chamber, from whence it is withdrawn. A 
coil of steam-pipe dd is provided for thawing ice and snow that 
may accumulate at the bottom of the chamber. Since the same 
air is used continuously, being taken from the cold room, chilled 
and returned, the effect of these devices is to remove the moist- 
ure from the air in the cold room and to maintain a cold, dry 
atmosphere in it, which is well adapted to preserving all kinds 
of perishable provisions. 

When an air-refrigerating machine is used as described the 
pressure in the cold room is necessarily that of the atmosphere, 
and the size of the machine is large as compared with its per- 



438 



THERMODYNAMICS OF THE STEAM-ENGINE, 



formance. The performance may be increased by running the 
machine on a closed cycle with higher pressures ; for example, 
the cold air may be delivered to a coil of pipe in a non-freezing 
salt solution, from which the air abstracts heat through the 
walls of the pipe and then passes to the compressor to be used 
over again. The machine may then be used to produce ice, or 
the brine may be used for cooling spaces or liquids. A machine 
has been used for producing ice on a small scale, without cool- 
ing water, on the reverse of this principle : that is, atmospheric 




Fig. 87. 



air is first expanded and chilled and delivered to a coil of pipe 
in a salt solution, then the air is drawn from this coil, after ab- 
sorbing heat from the brine, compressed to atmospheric pres- 
sure, and expelled. 

Calculation of Air-refrigerating Machine. — The per- 
formance of a refrigerating machine may be stated in terms of 
the number of thermal units withdrawn in a unit of time, or 
in terms of the weight of ice produced. The latent heat of 
fusion of ice may be taken to be 80 calories or 744 B. T. U. 

Let the pressure at which the air enters the compression 
cylinder be/^ , that at which it leaves be/^ ; let the pressure at 



REFRIGERATING MACHINES. 439 

cut-off in the expanding cylinder be p^ and that of the back 
pressure in the same be p^ ; let the temperatures corresponding 
to these pressures be t^, t^, t^, and Z^, or reckoned from the 
absolute zero, T^,T^, T^, and T^ . With proper valve-gear and 
large, short pipes communicating with the cold chamber,/^ 
may be assumed to be equal to p^, and equal to the pressure in 
that chamber. Also /^ may be assumed to be the temperature 
maintained in the cold chamber, and ^3 may be taken to be the 
temperature of the air leaving the cooler. With a good cut- 
off mechanism and large passages p^ may be assumed to be 
nearly the same as that of the air supplied to the expanding 
cylinder. Owing to the resistance to the passage of the air 
through the cooler and the connecting pipes and passages, p^ 
is considerably less than p^ . 

The expansion in the expanding cylinder may be assumed 
to be adiabatic, so that 

?:=l:r (3.6) 

Were the compression also adiabatic, the temperature /g 
could be determined in a similar manner ; but the air is usually 
cooled during compression, and contains more or less vapor, so 
that the temperature at the end of compression cannot be de- 
termined from the pressure alone, even though the equation of 
the expansion curve be known. 

Let the air passing through the refrigerating machine per 
minute be M, then the heat withdrawn from the cold room is 

Q,=Mc,{t,-t,) (327) 

The work of compressing M units of weight of air from the 
pressure/i to the pressure/j in a compressor without clearance is 

-^A.„-^4(jf -i}. . (3.8) 



440 THERMODYNAMICS OF THE STEAM-ENGINE. 

provided that the compression curve can be represented by an 
exponential equation. The work will be the same for a com- 
pressor with clearance if the exponent for the equation to the 
expansion curve is the same as that for the compression curve. 
If the compression can be assumed to be adiabatic, 

pr. = ^A-.^^{(J)^'-i}=fU-..); . (329) 

for in such case we have the equations 

K - I 

Y — \~p\ > ^^ = Cp—C^ = Cp — . 

The work done by the air in the expanding cylinder should 
be calculated in the manner used on page 201 in designing a 
steam-engine, or on page 325 for finding the work of a com- 
pressed-air engine. If the expansion and compression are 
both complete, then the work done by M units of weight of air is 

^. = ^'(^3-0 ..... (330) 

The work that must be supplied per minute is 

and the net horse-power required is 

W 

H. P.; 



33000 



but the gross horse-power required is much larger, since all the 
frictional resistances must be overcome, including the friction 
of both pistons. The proper allowance can readily be deter- 
mined on a machine with a steam-engine coupled direct, by in- 
dicating both of the air-cylinders and the steam-cylinder 
simultaneously. 



REFRIGERATING MACHINES. 441 

The heat carried away by the cooling water is 

Q^Q.^AW, (331) 

If compression and expansion are both adiabatic, then 

Q = Mc,{t, -i^J^t,-t,-t, + O = Mc,{t, - Q. (332) 

If the initial and final temperatures of the cooling water are 
/,• and tk , and if qi and qk are the corresponding heats of the 
liquid, then the weight of cooling water per minute is 

G = —^ (333) 

A good supply of cooling water and a method of regulating 
it should be provided, so that an approximate calculation may 
be made for any case, under the assumption of adiabatic com- 
pression and expansion, by the equation 

G^^f^ (334) 

Qk — <li 

The volume of the compression piston displacement, neglect- 
ing clearance, is 

^' 2n 2np,T, ' 2np, ' ' * ' ^•5i5; 

in which n is the number of revolutions per minute, and /„, v^, 
T^ are the pressure, volume, and absolute temperature, at at- 
mospheric pressure and at freezing-point. 

If it be assumed that p^ is the same as /, , then the volume 
of the expanding cylinder, without clearance, may be assumed 
to be 

v. = Ky (336) 



442 THERMODYNAMICS OF THE STEAM-ENGINE, 

If the clearance of the compressor is -— of the piston dis- 
placement, then the volume of air in the cylinder when the 
inlet-valve opens is 






and the volume calculated by equation (335) should be multi- 
plied by 

'+^(7;) -m- (337) 

If the expansion and compression in the expanding cylinder 
are complete, the same expression may be used to allow for 
clearance in that cylinder, making n equal to k. To allow for 
loss of pressure in valves and passages and for other imperfec- 
tions, both of these volumes may be increased by an amount 
to be determined by experirnent. In practice the expansion 
is seldom carried down to the back pressure in the expanding 
cylinder, nor is the compression complete, and the volume is 
smaller than that given by equation (336). 

The temperature T^ may be controlled by the cut-off of the 
expanding cylinder, and thus the performance of the machine 
may be varied. As the cut-off is shortened p^ is increased and 
7*4 diminished, and this in turn makes Vg smaller compared 
with V,. 

Problem. — Required the dimensions of an air-refrigerating 
machine to produce an effect equal to the melti»g of 200 pounds 
of ice per hour. Let the pressure in the cold chamber be 14.7 
pounds and the temperature 32° F. Let the pressure at cut- 
off in the expanding cylinder be 29.4 pounds by the indicator 
or 44.1 pounds absolute. Let the delivery pressure in the com- 
pressor be 39.4 pounds by the indicator, i.e., let the loss of pres- 
sure in the cooler and passages be 10 pounds. Let the initial 
and final temperatures of the cooling water be 60° and 80° F., 



REFRIGERATING MACHINES. 443 

and the temperature of the air from the cooler 90° F. Let the 
machine make 60 revolutions per minute. 

The melting of 200 pounds of ice per hour is equivalent to 
28800 B. T. U. per hour, or 480 B. T. U. per minute. 

Assuming adiabatic compression and expansion, 



T, = 492.7 QJl) ^'^ = 360 ; .-. t,= - ioo°.7 F. ; 



7; = 492.7 (yJ^) ^'' = 714.9 ; .-. h = 254^2 F. 

The air used per minute is therefore 

480 -r- (32 -j- 100.7) X 0.2375 = 12.10 pounds. 

The horse-power of the compression cylinder with adiabatic 
compression is 

W, _ 12.1 X 77^ X 0.2375 X ( 254.2 - 32) ^ ^ ^ ^^ p 



33000 33000 

If the compression curve may be represented by 
^^1.2 _ const., 

then the work of compression will be 

0.2 
1.2 ( /54.i\ 1-2 ) 
W, = 12.1 X 144 X 14.7 X 12.4 X --| [—-) - I ^ 

= 49230 foot-pounds, 

and the horse-power is therefore 14.0. 

The horse-power of the expanding cylinder is 

W, I2.I X 778 X 0.2375 X (32+1007) ^^xrp 

= y.O rl. Jr. 



33000 33000 



444 THERMODYNAMICS OF THE STEAM-ENGINE. 

The net horse-power required is therefore 6 H. P. or 5 H. P., 
and the indicated horse-power of the steam-cyHnder may be 
assumed to be 8 H. P. or 6f H. P., according to the manner of 
the compression. 

The volume of the compressor-piston displacement without 
clearance will be 

12.1 X 12.4 , . , ^ 
= 1.25 cubic feet. 

120 ^ 

The volume of the expanding cylinder under the same con- 
dition is 

1.25 X = o.Qi cubic feet. 

If the clearance of the compressor be assumed to be 0.02, 
the piston displacement should be 



1.2 



I 
5 j I + 0.02 f — ^j — 0.02 [ = 1.4 cubic feet. 



If the clearance of the expanding cylinder be assumed to 
be 0.05, the piston displacement should be 

0.91 j I + 0.05 f — ^j — 0.05 f = 0.96 cubic foot. 

If, further, an allowance of ten per cent be made for imper- 
fections, the dimensions may be: diameter, compressor, 17 
inches; diameter, expanding cylinder, 14 inches; stroke, 12 
inches. 

Compression-refrigerating Machine. — The arrangement 
of a refrigerating machine using a volatile liquid and its vapor 
is shown by Fig. 88. The essential parts are the compressor 
A^ the condenser B^ the valve Z>, and the vaporizer C. The 
compressor draws in vapor at a low pressure and temperature, 
compresses it and delivers it to the condenser, which consists of 
coils of pipe surrounded by cooling water that enters at e and 



REFRIGERATING MACHINES. 



445 



leaves at /. The vapor is condensed, and the resulting liquid 
gathers in a reservoir in the bottom, from whence it is led by 
a small pipe having a regulating valve D to the vaporizer or 
refrigerator. The refrigerator is also made up of coils of pipe, 
and is immersed in a non-freezing solution of salt, commonly 
chloride of calcium. The volatile liquid vaporizes and withdraws 
heat from the surrounding brine, and reduces the temperature 



H 



^. 



1/ 



1 



J 



Fig. 88. 



below the freezing-point of water. In the figure the machine 
is represented to be applied to ice-making, the water being in- 
troduced and frozen in properly-shaped moulds of thin metal. 
When the machine is used to cool a room the vaporizer may 
be made up of a system of pipes arranged to withdraw heat 
from the air, or brine may be cooled and circulated through 
such a system of pipes. When brine is used either in ice-mak- 
ing or in cooling, a positive circulation should be given it by a 
pump or the equivalent. 

In Fig. 88 the compressor is represented as single-acting, 
but for horizontal machines it is commonly made double-act- 



44^ THERMODYNAMICS OF THE STEAM-ENGINE. 

ing. Frequently the compressor has two single-acting vertical 
cylinders driven by a horizontal steam-engine coupled to the 
shaft. Such compressors sometimes have the clearance filled 
with oil, of which part is forced through the delivery-valves 
and allowed to flow back into the cylinder during the inflow 
of vapor. In any case, it is of great importance that the clear- 
ance shall be reduced to the smallest amount possible. 

To make the cycle of the machine complete the liquid from 
the condenser should be allowed to do work in an expansion 
cylinder like that of an air-refrigerating machine, instead of 
flowing through^ the regulating valve i?. The size of such a 
cylinder would be small, and the work recovered, insignificant, 
so that none of the machines in use are provided with such an 
expansion cylinder. 

Calculation of Compression Machine. — Let the pressure 
in the condenser be p^ , the temperature t^ , and the heat of the 
liquid q^ . Let the pressure in the vaporizer or refrigerator be 
p^ , the temperature t^ , and the total heat of vaporization \, 
The heat withdrawn from the refrigerant to change one unit of 
weight of liquid at the temperature t^ into saturated vapor at 
the pressure p^ is 

so that the heat withdrawn per minute by a machine using M 
units of weight of the working fluid per minute is 

Q,^M{K-q:) (338) 

Even though the compressor cylinder be water-jacketed, 
the walls are at a considerably higher temperature than the 
entering vapor, and the pressure during admission is a little 
lower than that in the vaporizer. Also most of the vapors 
now used in such machines are superheated by adiabatic com- 
pression. Therefore it is probable that the vapor is super- 
heated during compression, even though it be moist as it leaves 
the vaporizer. For an approximate calculation it may be 
assumed that the pressure in the cylinder during admission is 
p^ , that the vapor is dry and saturated at the beginning of 



REFRIGERATING MACHINES. 447 

compression, and that it is compressed adiabatically and super- 
heated during the entire compression. It will be shown that 
ammonia and sulphur dioxide, when moderately superheated, 
have the approximate characteristic equation 

pv = BT-Cp^-, (339) 

and that during an adiabatic change we have the equation 

T'={$r (^^°> 

During the expulsion of vapor from the compressor the 
pressure in the cylinder is a little higher than in the condenser, 
but it may be assumed to be the same for our approximate 
calculation. The temperature of the vapor leaving the com- 
pressor and entering the condenser may consequently be cal- 
culated by the equation 






(fr <-> 



The heat that must be withdrawn by the cooling water is 
therefore 

Q=:M\c,{t,-t,) + r,\ (342) 

in which Cp is the specific heat of the superheated vapor at 
constant pressure, and r^ is the heat of vaporization at the 
pressure p^ . 

If the initial and final temperatures of the cooling water are 
ti and tk , and if (/,• and Qk are the corresponding heats of the 
liquid for water, then the weight of cooling water used per 
minute is 

= "^^^=^ (3«, 



448 THERMODYNAMICS OF THE STEAM-ENGINE. 

For the first approximation the horse-power of the com. 
pressor may be calculated by the expression 

778xii/ja/,-/.) + ;i.-Aa 

33OCX) .... V344/ 

The power thus calculated should be multiplied by a factor 
to be found by experiment, in order to find the probable indi- 
cated horse-power of the compressor, and the indicated horse- 
power must be multiplied by another factor to find the power 
required to drive the machine, or by a factor to find the indi- 
cated horse-power of a steam-engine coupled to the shaft 
driving the compressor. 

If the actual pressures in the cylinder of the compressor 
during admission and delivery are p" and p' , if the specific 
volume at the beginning of compression is v" , and if the com- 
pression and expansion curves may be represented by the 
equation 

then the horse-power of the compressor may be found by the 
expression 



Mp"v" 
33000 



^,!(fr-}----(-) 



If the vapor at the beginning of compresssion can be 
assumed to be dry and saturated, then the volume of the 
piston displacement of a compressor without clearance, and 
making N strokes per minute, is 

^=^ (346) 

To allow for clearance, the volume thus found may be mul- 
tiplied by the factor 



m \pj m 



REFRIGERATING MACHINES. 449 

in which — is the clearance expressed as a fraction of the 
in 

piston displacement. The volume thus found is further to be 
multiplied by a factor to allow for inaccuracies and imperfec- 
tions. 

The vapors used in compression machines are liable to be 
mingled with air or moisture, and in such case the performance 
of the machine is impaired. To allow for such action the size 
and power of the machine must be increased in practice above 
those given by calculation. It would appear that proper pre- 
cautions ought to be taken to prevent such action from be- 
coming of importance. 

Problem. — Required the dimensions of an ammonia-refrig- 
erating machine to produce 2000 pounds of ice per hour. Let 
the temperature of the salt solution be 14° F. and the temper- 
ature in the condenser 86° F. ; let the initial and final temper- 
atures of the cooling water be 60° and 80° F. Let the compres- 
sor be double-acting, and let it make 60 revolutions per minute. 

The pressures corresponding to the temperatures 14° and 
86° are 41.5 and 168.2 pounds, absolute, per square inch, or 
26.8 and 153.8 pounds by the gauge. For ammonia, /^ = f . 
Hence by equation (341) 

r, = (14 + 460.7) (^)'- 673.7; 

/, = 2i3°F. 

If 5 per cent be allowed for ice wasted in removing it from 
the moulds, and for other losses, the capacity of the machine 
per minute must be 

2100 X 144 ^ ^ ^, 
g^-^ = 5040B.T.U.; 

.-. Q, = 5040 - M{k, - q,) = J/(554 - 59); 

5040 
/. M = = 10.2 pounds. 

495 ^ 



450 THERMODYNAMICS OF THE STEAM-ENGINE. - 

The heat withdrawn by the cooling water is 

Q = 10.210.508(213 - S6) + 49;} = 5727 B. T. U. 
The cooHng water required per minute is, consequently, 

Qk — % 48.09 — 28.12 ' ^ 

The horse-power will be, approximately, 

*j^%M\cit,-t:)-^\-K\ 

33000 

778 X io.2Jo.5o8(2i3 - 86) + 556 - 297} 

= — - 77 j5 

33000 '' 

The horse-power of the steam-cylinder may be assumed 
to be 

77.8 -^ 0.80 — 97.2. 

On the assumption that the vapor in the compressor is dry 
and saturated at the beginning of compression, the volume of 
the piston displacement, not allowing for clearance, is 

^^ Mv^ 10.2 X 7-05 1 • r . 

V—-^ = -pr-^~ 5-15 cubic feet. 

N 2 X 60 ^ ^ 

If we allow 10 per cent for the effect of clearance and im- 
perfect action, then the volume should be 5.7 cubic feet, or 
about 2o|- inches in diameter by 30 inches stroke. 

Fluids Available. — The fluids that have been used in 
compression-refrigerating machines are ether, sulphurous acid, 
ammonia, and a mixture of sulphurous acid and carbonic acid, 
known as Pictet's fluid. The pressures of the vapors of these 
fluids at several temperatures, and also the pressure of the 



REFRIGERATING MACHINES. 



451 



vapors of methylic ether and carbonic acid, are given in the 
following table : 

Pressures of Vapors, mm. of Mercury. 



Temperatures, 

degrees 

Centigrade. 


Ether. 


Sulphur 
Dioxide. 


Methyl- 
ether. 


Ammonia. 


Carbon 
Dioxide. 


Pictet's 
Fluid. 


- 30 





287.5 


576.5 


866.1 





585 


— 20 


68.9 


479-5 


882.0 


1392. I 


15142 


745 


— ID 


114. 7 


762.5 


1306.6 


2144.6 


20340 


1018 





184.4 


1165.1 


1879.0 


3183-3 


26907 


I3pi 


10 


286.8 


1719.6 


2629.0 


4574-0 


34999 


1938 


20 


432.8 


2462. I 


3586.0 


6387.8 


44717 


2584 


30 


634.8 


3431.8 


4778.0 


8701.0 


56119 


3382 


40 


907.0 


4670.2 





II595.3 


69184 


4347 



Ether was used in the early compression machines, but at 
the temperatures maintained in the refrigerator the pressure is 
small and the specific volume large, so that the machines, like 
air-refrigerating machines, were either feeble or bulky. More- 
over, air was liable to leak into the machine and unduly heat the 
compressor cylinder. Sulphur dioxide has been used success- 
fully, but it has the disadvantage that sulphuric acid may be 
formed by the leakage of moisture into the machine, in which 
case rapid corrosion occurs. Ammonia has been extensively used 
in the more recent machines with good results. When distilled 
from an aqueous solution it is liable to contain considerable 
moisture. As is shown by the table, Pictet's fluid has a pressure 
at low temperature intermediate between the pressures of 
sulphur dioxide and ammonia, and the pressure increases slowly 
with the temperature. 

The properties of saturated vapor of ether were determined 
by Regnault, and are given in Chapter VII. For the other 
vapors given in the table (except Pictet's fluid) he determined 
the relations of the temperature and pressure, but not the 
total heat of vaporization nor the heat of the liquid. He did, 
however, determine some of the properties of these substances 
in the gaseous state, or more properly, in the state of super- 
heated vapors. It was first proposed by Ledoux * that the 



* Annales des Mines, 1878. 



452 THERMODYNAMICS OF THE STEAM-ENGINE. 

properties of the superheated vapors of sulphur dioxide and 
ammonia can be represented by equations of the form deduced 
by Zeuner for superheated steam, and that the appHcation of 
these equations to the saturated vapors as the limit makes it 
possible to calculate the properties of the saturated vapors 
approximately. His equations do not fulfil the conditions 
given by equation (i66), page Ii8, and do not represent all the 
properties of the superheated vapors, given by Regnault ; conse- 
quently new equations have been calculated for both French 
and English units. 

Properties of Sulphur Dioxide. — The specific heat of 
gaseous sulphur dioxide is given by Regnault* as 0.15438, and 
the coefficient of dilatation as 0.0039028. The theoretical spe- 
cific gravity compared with air, calculated from the chemical 
composition, is given by Landolt and Bornsteinf as 2.21295. 
Gmelin % gives the following experimental determinations : by 
Thomson, 2.222 ; by Berzelius, 2.247. The figure 2.23 will be 
assumed in this work, which gives for the specific volume at 
freezing-point and at atmospheric pressure 






cubic metres. The corresponding pressure and temperature 
are 10333, and 273^7 C. 

Now the coefficient of dilatation is the ratio of the increase 
of volume at constant pressure, for one degree increase of tem- 
perature, to the original volume. Writing the equation (166), 



pv = ^aT-Cr; (347) 



*M6moires de I'lnstitut de France, Tome xxi., xxvi. 

f Physikalische-chemische Tabellen. 
X Watt's translation, p. 280. 



REFRIGERATING MACHINES. 453 

we have at o° C. and i° C, 





A^o 




^r,~ 


-cpr, 




A^i 





^r,- 


-cpr, 


^1 


-"^0 


_^>^ 


a 





V, A' p,v^ ' 

Substituting the known values and solving for a, we obtain 
0.2I2; but the equation obtained from the equation (347) with 
this figure does not agree well with Regnault's experiments on 
the compressibility of sulphur dioxide. If, instead, we make 

a = 0.22, 

then by equation (347) the coefficient of dilatation becomes 
0.00404, and it will be shown later that the equation deduced 
with this value agrees quite well with the experiments on com- 
pressibility. 

The coefficient of T in equation (347) is therefore 

0.15438 X 426.9 X 0.22 = 14.5, 

and the coefficient of /* is 

14-5 X 2737 - 10333 X 0.347 ^ , 

=^2 = 48 nearly; 

10333 

so that the equation becomes 

pv=:i4.ST-4Sf-'' (348) 

Regnault found for the pressures 

p^ = 697.83 mm. of mercury, 
A =1341.58 " 



454 THERMODYNAMICS OF THE STEAM-ENGINE, 

and at 7°./ C. the ratio 



/.^« 



= 1.02088. 



Reducing the given pressures to kilograms on the square 
inch, and the temperature to the absolute scale, and applying to 
equation (347), we obtain instead of the experimental value for 
the above ratio 1.016. 

Regnault gives for the pressure of saturated sulphur diox- 
ide, in mm. of mercury, the equation 

log p = a — ba^ — eft"" ; 

a = 5.6663790 ; 
log 3 = 0.4792425 ; 
log c = 9.1659562 — 10; 
log a = 9.9972989 — 10 ; 
log J3 = 9.98729002 — 10 ; 

;2 = ^ + 28° C. 

Applying equations (109) and (no), page 80, to this case, 



I dp 
p dt~ 


-. Aa^-\-Bp'\ 


log a- 
log/5 = 
log^ = 


: 9.9972989; 
-- 9-98729002 ; 
18.6352146; 


log^ = 

n — 


: 7-9945332 ; 

:/+28°C. 



The specific volume of saturated sulphur dioxide may be 
calculated by inserting in equation (347) for the superheated 
vapor the pressures calculated by aid of the above equation. 
The results at several temperatures are as follows : 

^ — 30° C. o + 30° C. 

s 0.8292 0.2256 0.0825 



REFRIGERATING MACHINES. 455 

Andr^eff* gives for the specific gravity of fluid sulphur 
dioxide 1.4336; consequently the specific volume of the liquid is 

(J = 0.0007. 

The value of r, the heat of vaporization, may now be calcu- 
lated at the given temperatures by equation (128), 

in which u=z s — cr. 

The results are 

t - 30° C. o + 30° C. 

r 106.9 97.60 90.54 

Within the limits of error of our method of calculation, the 
value of r may be found by the equation 

r = 98 — o.27^f. 

To find the specific heat of the liquid, we may use equa- 
tion (180), page 120, 

/ T dp\ dr r 

At 0° C. the specific heat is approximately 

c = 0.4. 

In English units we have for superheated sulphur dioxide 

pv = 26.4T— 184/°-% 

the pressures being in pounds on the square foot, the volumes 
in cubic feet, and the temperatures in Fahrenheit degrees 
absolute. 

*Ann. Chem. Pharm. 1859. 



45^ THERMODYNAMICS OF THE STEAM-ENGINE. 

For pressures in pounds on the square inch at temperatures 
on the Fahrenheit scale, 

log/ — a — ba'' — c§'^\ 

^==3-9527847; 
log b = 0.479242 s ; 
log c = 9.1659562 — 10; 
log a = 9.9984994 — 10 ; 
log /3 = 9.99293890 — 10 ; 

;2 = /-f i8°.4 F. 

For the heat of vaporization 

r = 1^6 — o,2'j{t — 32), 

and for the specific heat of the liquid 

c = 0.4. 

Properties of Ammonia. — The specific heat of gaseous 
ammonia, determined by Regnault, is 0.50836. The theoretical 
specific gravity compared with air, calculated from the chemical 
composition, is given by Landolt and Bornstein as 0.58890. 
Gmelin gives the following experimental determinations: by 
Thomson, 0.5931 ; by Biot and Arago, 0.5967. For this work 
the figure 0.597 will be assumed, which gives for the specific 
volume at freezing-point and at atmospheric pressure 

0.597 ^ 

cubic meters. The coefficient of dilatation has not been de- 
termined, and consequently cannot be used to determine the 
value of a in equation (347). It, however, appears that very 
consistent results are obtained if a is assumed to be i, as for 
superheated steam. The coefficient of T then becomes 

0.50836 X 426.9 X i= 54-3» 



REFRIGERATING MACHINES. 457 

and the coefficient of /* is 

54.3 X 273.7-10333 X 1.30 _ ,.^. 
— 142 , 

10333 
so that the equation becomes 

/z/= 54.37^- 142/i (349) 

The coefficient of dilatation, calculated by the same process 
as that used in determining a for sulphur dioxide, is 0.00404, 
which may be compared with that for sulphur dioxide. 

Regnault found for the pressures 

p^ = 703.50 mm. of mercury, 
A = 1435.3 " 
and at 8°.i C. the ratio 



A^. 



1.0188, 



while equation (349) gives under the same conditions 1.0200. 
For saturated ammonia Regnault gives the equation 

log/ = a — da"" — c/S""; 

a= 11.5043330; 
log 3 = 0.8721769; 
log c = 9-9777087 - 10 ; 
log a = 9.9996014 — 10; 
log ^ = 9.9939729 - 10 ; 

n = t -\- 22° C. ; 

by aid of which the pressures in mm. of mercury maybe calcu- 
lated for temperatures on the Centigrade scale. The differen- 
tial coefficient may be calculated by aid of the equation 

I dp 



45 S THERMODYNAMICS OF THE STEAM-ENGINE, 

log ^ = 8.1635 170 — lO; 
log B — 8.4822485 — 10 ; 
log a — 9.9996014 — 10; 

log fi = 9-9939729 - 10 ; 

n = t-\-22°C. 

The specific volume of saturated ammonia calculated by 
equation (339) at several temperatures are 

if - 30° C. o + 30° C. 

s 0.9982 0.2961 0.1 167 

Andreeff gives for the specific gravity of liquid ammonia at 
0° C, 0.6364, so that the specific volume of the liquid is 

(T = 0.0016. 

The values of r at the several given temperatures, calculated 
by equation (128), are 

2f -30° C. o + 30° C. 

r 325.7 300.15 277.5 

which may be represented by the equation 

, r = 300 — 0.8 A 

The specific heat of the liquid, calculated by aid of equa- 
tion (180), is 

c = I.I. 

In English units the properties of superheated or gaseous 
ammonia may be represented by the equation 

pv =: ggT — 540/i, 

in which the pressures are taken in pounds on the square foot 
and volumes in cubic feet, while T represents the absolute 
temperature in Fahrenheit degrees. 



REFRIGERATING MACHINES. 459 

The pressure in pounds on the square inch may be calcu- 
lated by the equation 

\ogp=.a — ba"" — cp^\ 

a = 97907380 ; 

log b = 0.8721769 — 10; 

log ^ = 9.9777087 - 10; 

log a = 9.9997786 — 10; 

log ^ = 9.9966516 — 10; 

n = t + f.6 F. 

The heat of vaporization may be calculated by the equation 

r = 540 — o.8(/ — 32), 
and the specific heat of the liquid is 

c = I.I. 

Pictet's Fluid. — Attention has already been called to the 
mixture of sulphur dioxide and carbon dioxide known as Pic- 
tet's fluid, which was adopted by Pictet for use in his refriger- 
ating machines after an extended investigation. The desirable 
properties are stated by him to be : 

1. The tension of the vapor should be greater than that of 
sulphur dioxide and less than that of ammonia. The boiling- 
point under atmospheric pressure should be about — 20°C. 

2. The tension of the vapor in the condenser at about 
-|- 30° C. should be between 7 and 8 atmospheres. 

3. The fluid should be incombustible. 

4. The fluid should not attack metals. 

5. The fluid should have such a chemical composition that 
changes of volatility during use need not be feared. 

6. The fluid should be of an unctuous nature, so that oil need 
not be used on the piston of the compressor. 

7. The fluid should be inexpensive. 

An investigation of the properties of various fluids shows 
that the addition of oxygen to any compound, whether it en- 
tered in solution or into chemical combination, diminished the 



4^0 THERMODYNAMICS OF THE STEAM-ENGINE, 

volatility. Thus carbon monoxide boils at — 140° C, while 
carbon dioxide boils at — 75° C. ; sulphur dioxide boils at 
— 10° C, and anhydrous sulphurous acid boils at -|- 32°, while 
the hydrate boils at -|- 326° C. Other examples are given by 
Pictet showing the same result. As a result of experiments on 
the mixture of sulphur dioxide and carbon dioxide he gives 
the following table of boiling-points. The formulae express 
the proportion of the elements in the mixtures, but are not to 
be taken to represent chemical compounds. 





Boiling--point. 




Boiling-point, 


c..o,,s 


-71° 


co,s. 


-15° 


c„o.,s 


-54° 


CO.S, 


- 12" 


c„o„s 


-41° 


co,.s. 


-9°-5 


C,oO,,S 


-26° 


co„s. 


-8°.6 


co.s 


-19° 


co.,s. 


-8° 






co„s, 


-7°.5 



The mixture, which may properly be expressed by the for- 
mula COj -|- SO2, was found to fulfil all the seven desirable 
properties, and, as is shown by the table on page (451), the 
pressure increases less rapidly with the temperature than for 
simple vapors, so that while the pressure at — 30° C. is double 
that of sulphur dioxide, the pressure at + 30° C. is a little 
less than that of that fluid. This remarkable property appears 
to be due to the increased solvent action of the two fluids on 
each other at higher pressures, which acts to diminish the 
mechanical work of compression from one temperature to 
another; for example, in the compressor of a refrigerating 
machine. 

Absorption Refrigerating Apparatus. — Fig. 89 gives 
an ideal diagram of a continuous absorption refrigerating ap- 
paratus. It consists of the following essential parts: (i) the 
generator B^ containing a concentrated solution of ammonia in 
water, from which the ammonia is driven by heat ; (2) the con- 
denser (7, consisting of a coil of pipe in a tank, through which 
cold water is circulated ; (3) the valve F", for regulating the pres- 
sures in Cand in /; (4) the refrigerator/, consisting of a coil of 



REFRIGERATING MACHINES. 



461 



pipe in a tank containing a non-freezing salt solution ; (5) the 
absorber A, containing a dilute solution of ammonia, in which 
the vapor of ammonia is absorbed ; and (6) the pump P for 
transferring the solution from the bottom of A to the top of 
B ; there is also a pipe connecting the bottom of ^ with the top 
of A. It is apparent that the condenser and refrigerator or 
vaporizer correspond to the parts B and C of Fig. 88, and 
that the absorber and generator take the place of the com- 



' 1 III 

1 III 

1 ' 'ir 


c 


f 


A 




>!—!--» 



Fig. 89. 

pressor. The pipes connecting A and B are arranged to take 
the most concentrated solution from A to B, and to return 
the solution from which the ammonia has been driven, from B 
to A, In practice the generator B is placed over a furnace, by 
which heat is applied to drive off the ammonia. Also, arrange- 
ments are made for transferring heat from the hot liquid flow- 
ing from B to A to the cold liquid flowing from A to B. As 
the ammonia is distilled from water in B the vapor driven off 
contains some moisture, which causes an unavoidable loss of 
efficiency. 

The earliest absorption apparatus, made by Carr^, consisted 
of a cylindrical receptacle containing a solution of ammonia, 
and acting alternately as generator and absorber, in open com- 
munication through a pipe with a vessel of double conical 
form, acting alternately as condenser and refrigerator. In use, 
the generator was placed on a furnace and the condenser in a 
tank of cold water, and the ammonia driven off from the solu- 
tion condensed between the inner and outer conical surfaces of 



462 THERMODYNAMICS OF THE STEAM-ENGINE. 

the condenser. When a sufficient amount of liquid ammonia 
had collected, the vessel containing the solution was transferred 
from the furnace to the cold-water tank, and became thereby 
changed into the absorber. The condenser at the same time 
became the vaporizer or refrigerator, and after receiving a 
mould containing water to be frozen, was securely wrapped 
with non-conducting material. Apparatus of this kind is only 
fitted for work on a small scale, and is inefficient. 

An adaptation of Carre's apparatus has been used in re- 
frigerator cars for carrying perishable freight. In the car are 
placed two receptacles — one containing liquid ammonia, which 
maintains a low temperature by vaporization ; and the other 
containing water, to absorb the ammonia as it is formed. At 
the end of the route, or when necessary, the receptacles are re- 
charged — one with liquid ammonia and the other with fresh 
water. The ammonia in the rejected solution is regained by 
distillation. 

Vacuum Refrigerating Apparatus. — A form of absorption 
apparatus uses water for the volatile liquid and concentrated 
sulphuric acid for the absorbent. From the fact that vapor of 
water at freezing-point has a very low tension, such apparatus 
are called vacuum apparatus. 

The first apparatus of this kind was designed for freezing 
water in carafes, and consisted of a good air-pump, and a re- 
ceptacle containing oil of vitriol. The carafe, well wrapped in 
non-conductor, was attached to a pipe leading to the sulphuric 
acid receptacle, the pump was worked till a good vacuum was 
produced, and the acid was stirred to present fresh acid to the 
vapor which rapidly streamed from the water at the low pres- 
sure produced. The vaporization of about one sixth of the 
weight of the water was found to be sufficient to freeze the 
remainder. 

An ideal sketch of a continuous vacuum apparatus is shown 
by Fig. 90. At B is an air-pump capable of producing a 
vacuum of one or two mm. of mercury, in the chamber ^C 
At H there is a tank of concentrated sulphuric acid, from which 
a spray is delivered at J. The acid absorbs the vapor found 



REFRIGERATING MACHINES. 



463 



in the chamber at the low pressure existing there, gathers in 
the tanky, and flows out through the pipe K, which is of suf- 
ficient length to deliver the acid against atmospheric pressure 



v^////////}////^ 




Fig. 90. 

in the tank L. The dilute acid is reconcentrated and returned 
to the tank H. At 6^ is a pipe supplying fresh water, which 
passes through the water-injector j, and throws a jet of salt 
solution into the chamber at A. The finely divided jet loses 
fresh water by vaporization, is chilled, and gathers in the bot- 
tom of the chamber. The salt solution flows through the pipe 
^in the cold chamber EE, taking up heat on the way, and is 
again thrown into the chamber with a fresh supply of water 
from the pipe G. At N and N are screens to prevent splash- 
ing of water into the upper part of the chamber. 

Schroter's Tests of Refrigerating Machines. — Professor 
M. Schroter* made a number of tests on various forms of re- 
frigerating machines, in the years 1 885-1 887, to determine the 
efficiency of such apparatus in practice. From his report the 
following tests have been taken : 

* Untersuchungen an Kaltemaschinen. 



464 



THERMODYNAMICS OF THE STEAM-ENGINE. 



Test of a Bell-Coleman Machine. — An air-refrigerating^ 
machine, constructed under the Bell-Coleman patents, was tested 
at an abattoir in Hamburg, where it was used to maintain a 
low temperature in a storage-room. The machine is horizontal, 
and has the pistons for the expansion and compression cylinders 
on one piston-rod, the expansion cylinder being nearer tl^e 
crank. Power is furnished by a steam-engine acting on a crank 
at the other end of the main shaft, and at right angles to 
the crank driving the air-pistons. Both the steam-cylinder and 
the expansion cyHnder have distribution slide-valves, with inde. 
pendent cut-off valves. The main dimensions are given in the 
following table : 

DIMENSIONS BELL-COLEMAN MACHINE. 



Steam 
Cylinder. 



Head 
end. 



Crank 
end. 



Compression 
Cylinder. 



Head 
end. 



Crank 
end. 



Expansion 
Cylinder. 



Head 

end. 



Crank 
end. 



Diameter of piston, cm 

" " piston-rod, cm 

Stroke, m 

Clearance, per cent of piston displacement, 



0.605 
S-9 



■^3 
6.9 
0.605 
5-8 



71 
9.0 
0.605 



71 
6.8 
0.605 



53 
9.0 
0.605 
8.9 



53 
9.0 
0.605 
8.9 



Water is sprayed into the compression cylinder, and the air 
is further cooled by passing through an apparatus resembHng 
a steam-engine jet condenser, after which it is dried by passing 
it through a system of pipes in the cold room before it passes 
to the expansion cylinder. 

In the tests indicators were attached to each end of the 
several cylinders, and the temperature of the air was taken at 
entrance to and exit from each of the air-cylinders. Speci- 
mens . of the indicator-diagrams from the air-cylinders show, 
for the compressor, a slight reduction of pressure during ad- 
mission and some irregularity during expulsion, and for the 
expansion cylinder, a little wire-drawing at cut-off, and a good 
expansion and compression, though neither are complete. No 
attempt was made to measure the amount and temperatures of 
the cooling water. 

The data and results of the tests and the calculations are 
given in Table XXXV. 



REFRIGERATING MACHINES, 



465 



TABLE XXXV. 

Tests on Bell-Coleman Machine. 



Number of Test 

Duration in hours 

Revolutions per minute 

Temperatures of air, degrees Centigrade: 

At entrance to compression cylinder 

At exit from " " 

At entrance to expansion " 

At exit from " '* 

Mean effective pressure, kgs. per sq. cm.: 

Steam-cylinder: head end 

crank end 

Compression cylinder: head end 

crank end 

Expansion cylinder : head end 

crank end 

Indicated horse-power: 

Steam-cylinder 

Compression cylinder 

Expansion cylinder 

Mean pressure during expulsion from compression cylinder, kgs. 
Mean pressure during admission to expansion cylinder, kgs.. . . 

Difference 

Calculation from compression diagram: 

Absolute pressure at end of stroke, kgs , 

Absolute pressure at opening of admission-valve, kg. : 

Head end 

Crank end 

Volume at admission, per cent of piston displacement: 

Head end 

Crank end 

Weight of air discharged per stroke, kg.: 

Head end 

Crank end 

Weight of air discharged per revolution, kg 

Calculation from expansion diagram: 
Absolute pressure at release, kgs.: 

Head end 

Crank end 

Absolute pressure at compression, kgs.: 

Headend 

Crank end 

Volume at release, per cent of p. d.: 

Headend 

Crank end 

Volume at compression, per cent of p. d.: 

Headend 

Crank end 

Air used per stroke, kg.: 

Headend 

Crank end : 

Air used per revolution 

Difference 01 weights, calculated by compression and expan- 
sion diagrams, kg 

In per cent of the former 

Mean weight of air per revolution, kg 

Elevation of temperature at constant pressiire, degrees Centi- 
grade 

Heat withdrawn per hour, calories 



I. 


II. 


6 


1.63 


65-05 


61.2 


19-3 
27-3 
19.0 


17-5 
26.8 
16.6 


-47.0 


- 47-0 


2.263 


2-336 


2.239 
1.900 
1.869 
1.592 


2.294 

1. 861 

1.825 

' 1-589 


1. 615 


1-594 


85.12 

128.85- 

60. ID 


82.35 
Z18.55 
56.12 


3-35 
2.82 


3-25 
2.83 


0.53 


0.42 


T.04 


1.04 


0.783 
0.765 


0.788 
0.749 


6.15 
8.50 


i:!^ 


0.2744 


0.2764 


0.2716 
0.546 


0.2742 
0-551 


1.32 


1. 31 


1-45 


1.44 


1. 14 


1. 14 


1.20 


1. 19 


104.65 
106. 1 


104 7 
106.3 


16.5 


16.0 


19.8 


19.6 


0.234 


0.233 


0.254 
0.488 


0.254 
0.487 


0.058 
10.6 


0.064 
II. 6 


0.514 


0.519 


66.3 


64-5 


371 


354 



III. 

2.92 

63-5 
19. 1 

27.2 

19. 1 
47.0 

2-343 
2.301 
1.870 
1.906 
1.626 
1.624 

85.71 
126.01 

59-46 
3-40 
2.84 
0.56 

1.04 

0.764 

0.765 

6.03 
7.91 

0.2750 
0.2730 
0.548 



104.8 
106.4 



[6.6 
20.6 



0.238 
0.255 
0.493 

0-055 



66.1 
363 



Tests of Compression Machines. — In Table XXXVI are 
given the data and results of tests on three refrigerating ma- 
chines on the Linde system using ammonia, and of a machine 
on Pictet's .system using Pictet's fluid. The tests on machines 
used for making icc were necessarily of considerable length, 



466 



THERMODYNAMICS OF THE STEAM-ENGINE. 



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468x THERMODYNAMICS OF THE STEAM-ENGINE. 

but the tests on machines used for coohng Hquids would be of 
shorter duration. 

The cooHng water when measured was gauged on a weir or 
through an orifice. In the tests 3 to 6 on a machine used for 
cooHng fresh water the heat withdrawn was determined by 
taking the temperatures of the water cooled, and by gauging 
the flow through an orifice, for which the coefficient of flow 
was determined by direct experiment. The heat withdrawn in 
the tests 7 and 8 was estimated by comparison with the tests 3 
to 6. The net production of ice in the tests i and 2 was deter- 
mined directly; and in the test 2 the loss from melting during 
the removal from the moulds was found by direct experiment 
to be 8.45 per cent. By comparison with this, the loss by 
melting in the first test was estimated to be J.J per cent. The 
gross production of ice in the refrigerator was calculated from 
the net production by aid of these figures. In the tests 9 to 
12 on the Pictet machine the gross production was determined 
from the weight of water supplied, and the net production 
from the weight of ice withdrawn. 

A separate experiment on the machine used for cooling 
brine gave the following results for the distribution of power: 

Total horse-power, 57.1 

Power expended on compressor, 19.5 

*' " " centrifugal pump, ..... 9.8 

" *' " water-pump, . 3.6 

The centrifugal pump was used for circulating the brine 
through a system of pipes used for cooling a cellar of a brew- 
ery. The water-pump suppHed cooling water to the condenser 
and for other purposes. 

A similar test on the Pictet machine gave : 

Power of engine alone, 7.9 H. P. 

'^ " engine and intermediate gear, . . 16.6 ^' " 
'' " engincj gear, and pump, .... 20.0 "■ '^ 
From the above data the following table was arranged for 
the several tests on this machine : 



REFRIGERATIXG MACHINES. 
INDICATED AND EFFECTIVE WORK. 



469 



Number of Test. 



Indicated work without compressor 

" " engine alone 

Effective work of steam-engine 

Indicated work of steam-engine 

Mechanical efficiency of steam-engine 

Power absorbed by intermediate gearing 

Power absorbed by compressor 

Indicated power of compressor 

Mechanical efficiency of compressor 



9 


10 


11 


12 


19.9 


20.0 


20.0 


19.9 


7-9 


8.0 


7 


9 


7-9 


77.1 


80.1 


84 


6 


94.4 


91.2 


94-5 


99 


2 


109.8 


0.84 


0.85 





«5 


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II. 2 


II 


2 


II. 2 


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68.9 


73 


4 


83.2 


52.0 


61.7 


<0i3 


4 


75 -o 


o.79(?) 


0.89 





90 


0.90 



Test of an Absorption Machine.—The principal data and 
the results of a test made by Professor J. E. Denton,^ on an 
absorption ammonia-refrigerating machine, are given in Table 
XXXVII. The machine is applied to chill a room of about 
400,000 cubic feet capacity at a pork-packing establishment at 
New Haven, Conn. In connection with this test the specific 
heat of the brine, which served as a carrier of heat from the 
cold room to the ammonia, was determined by direct experi- 
ment. The brine chilled and the cooling water used were 
measured with meters, which were afterwards tested under the 
conditions of the experiment. 

TABLE XXXVII. 
Test of an Absorption Machine. — Seven Days' Continuous Test, 

Sept. 11-18, 1888. 



Generator. 



. f Genera 

Average pressures I g^^^^ 

above atmosphere -( pQQjgj. 

in lbs. per sq. in. [^Absorber! 



Average tempera- 
tures in Fahren- 
heit degrees. 



Atmosphere in vicinity of machine. 
Generator 

j Inlet 

( Outlet. 



Brine 



^ , { Inlet. . 

Condenser -j ^^^j^^ 

., , ( Inlet 

Absorber JQ^^j^^^^ 



i Upper outlet to generator 

Heater •< Lower " "absorber 

( Inlet from absorber 

Inlet from generator 

Water returned to main boilers from steam 
coil 



150.77 
47.70 
23.69 
23-4 

80 
272° 

21. 20'^ 

i6.i6~ 

54i 

80 

80 
III 
212 
178 
132 
272° 

260 



* Trans. Am. Soc. Mech. Eng., vol. x., May, 



470 



THERMODYNAMICS OF THE STEAM-ENGINE. 



Average range of ( Condenser, 
temperatures"! Absorber. . 
Fahr. degrees. ( Brine 



Brine circulated per j Cubic feet, 
hour. \ Pounds. . . 



Specific heat of brine 

Cooling capacity of machine in tons of ice per day of 24 hours. . 

Steam consumption per hour, to volatilize ammonia, and to 

operate ammonia pump lbs. 



5 Per pound of brme. 



British 
units. 



thermal 



Eliminated 1 -^ ^ 1 , 

{ iotal per hour 

Of refrigerating effect per pound of steam 

consumption 

D •r.r.^^A S At condenser, per hour 

R^J^^^^^i At absorber " 

f On entering genera- 

Per pound of steam \ ^ ^^\ ^°\^ 

^ j On leavmg genera- 
ls tor coil 

Consumed by generator per lb. of steam 

condensed 



Condensing water per hour, in lbs 

Equivalent ice production per pound of coal, if one pound of 

coal evaporates ten pounds of steam at boiler 

Calories, refrigerating effect per kilogramme of steam consumed. 
. . , . 1 ( Condensing coil 

Approximate c o 1 1 ^ Absorber 
surface m sq. ft 



Steam 



r 



Sizes, in inches, of 
duplex pumps. 



Ammonia pump 



Brine 



Dia. steam cyl. . . 

" ammonia cyl. 

Stroke 

Dia. stean." cvl. . . . 

" brine 
Stroke. 



Total revolutions j Ammonia pump, one. . , 

per minute. l Brine pump, two 

Effective stroke of pumps, part of full stroke, 



25i ' 

31 

5.13 

1,633.7 

119,260 

0.800 

40.67 
1,986 
4.104 

481,260 

243 

918,000 
.116,000 

1,203 

271 

932 

36,000 

17. 1 

T35 
870 
350 
200 

9 

3f 
10 

9i 
8 
10 



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0.8 



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